Straight lines Questions and Answers

cost Susana has organized information about banquet costs on a graph for her school Use her graph to answer the questions 5500 5000 4500 4008 3500 3000 2500 2000 1500 1000 500 25 50 75 100 125 150 175 number of people served Bella s Luci s point where both companies charge the same amount Enter 4 digit dollar amounts without a comma Enter the correct answer 00 DONE

Examine the properties listed below Determine which of the following properties are true for all parallelograms Select three that apply A four right angles B C D E diagonals bisect each other opposite sides are congruent opposite angles are congruent diagonals intersect at right angles

Dividing a Line Segment Mastery Test Drag the tiles to the correct boxes to complete the pairs Not all tiles will be used Directed line segments AC DF and PQ are shown on the graphs Match each graph with the ratio in which the directed line segment is partitioned Next 3 2 3 1 1 1 4 2 1 4 B 4 2 2 D 4 12 y 2 4 4 2 S 4 1 2 4 4 x Submit Test Tools Info

The graph shows the approximate U S box office revenues in billions of dollars from 2000 to 2012 where z 0 represents the year 2000 U S Box Office Revenue Y 10 8 Revenue billions of dollars 02 4 6 8 10 12 x Year 0 2000 a Estimate the slope and y intercept of the graph Slope 1 intercept b Interpret your answers in part a in the context of the problem The approximate U S box office revenue Increased by about 0 22 billion each year from 2000 to 2012 and was 4 billion in 2000 The approximate U S box office revenue increased by about 0 22 billion each year from 2000 to 2012 and was 8 billion in 2000 The approximate U S box office revenue Increased by about 0 4 billion each year from 2000 to 2012 and was 8 billion in 2000 The approximate U S box office revenue Increased by about 4 billion each year from 2000 to 2012 and was 8 billion in year 2000 c How can you use your answers in part a to predict the U S box office revenue in 2018 O Write a linear model in slope intercept form then substitute 18 for y and solve for z Write a linear model in slope intercept form then substitute 18 for 2 and solve for y O Multiply the slope by 18 to predict the revenue There is no way to make a prediction because the rate of change is not constant

The relationship between the number of pounds lb of cereal and the price in dollars is shown in the graph What is the unit price of cereal Price dollars 35 28 21 14 7 2 4 Weight pounds O A OB 1 lb 7 O C 16 OD 7 1 lb 3 5

The following data show the list price x in thousands of dollars and the dealer invoice price y also in thousands of dollars for a variety of sport utility vehicles Find a linear equation that approximates the data using the points 16 5 16 1 and 20 0 18 3 Round to two decimal places as needed List Price Dealer Invoice Price 16 5 17 6 20 7 23 1 20 0 24 6 16 1 17 0 18 2 19 3 18 3 21 0 O A y 0 63x 5 73 OB y 0 63x 6 38 O C y 1 59x 10 21 O D y 1 59x 9 11

The following graph shows the approximate relationship between speed in miles per hour and feet per second Answer parts a through e Feet per second AF 160 120 80 40 04 0 100 147 40 80 Miles per hour a Determine the slope of the line The slope of the line is 1 47 Type an integer or decimal rounded to the nearest hundredth as needed b Determine the equation of the line 120 M Q The equation of the line is F 0 Type an expression using M as the variable Use integers or decimals for any numbers in the expression Round to the nearest hundredth as needed

The graph below represents one equation in a system of equations with the solutions 4 0 and 0 4 Determine which linear equation completes the system Oy x 4 o x y 4 O y x 4 x y 4 2 2 2 2 X

Hans is planting a garden with snapdragons and daisies The table shows some possible combina of the two plants If Hans plants 29 daisies how r snapdragons will he plant models the scenario The equation Hans will plantsnapdragons

Select all the correct locations on the graph If we draw lines to join each given point to the origin identify the points whose corresponding line has a slope that is an integer value y 10 9 8 7 6 01 5 3

Suppose a vine maple grows in height linearly Four weeks after it is planted it stands 7 8 inches and after nine weeks it is 13 8 inches tall Write an equation that models the growth in inches of the vine maple as a function of time in weeks 1 What is the slope of the function 2 How tall was the tree when it was first planted 3 Write the function G w 4 How tall will the vine maple be after 16 weeks If needed round to 2 decimal places

Anumeha is mowing lawns for a summer job For every mowing job she charges an initial fee of 10 plus a constant fee for each hour of work Her fee for a 5 hour job for instance is 35 Let y represent Anumeha s fee in dollars for a single job that took x hours for her to complete

Finish the following phrases to identify angles as congruent or if they are supplementary add to 180 Alternate Interior angles Alternate Exterior angles Corresponding angles Consecutive angles Solve for x in the images below and show your work for full credit x 88 x 108 7x 6 Z 8x 1

ine pis perpendicular to line q Drag and drop the correct answers to the boxes below to complete the sentence If the equation of line p is 2x 5y 10 then the equation of line q must be x 2y 12 because perpendicular lines have slopes with a product of

15 O a 2b a 2b a 2b N Given The coordinates of rhombus WXYZ are W 0 4b X 2a 0 Y 0 4b and Z 2a 0 Prove The segments joining the midpoints of a rhombus form a rectangle As part of the proof find the midpoint of YZ a 2h W Y X

Every month Midtown Grocery Store donates 8 ounce cans of vegetables to a food bank The food bank s volunteers fill bags with these cans and deliver the bags to families in need This graph shows the relationship between the number of bags the food bank s volunteers can fill x and the total number of cans they deliver y 20 Cans 18 16 14 12 10 8 9 4 2 2 5 Bags Do x and y have a proportional relationship yes no 3 6 7 8 9 10 What is the constant of proportionality Write your answer as a whole number or decimal

3 P 1 according to the partial construction shown what is the next step in constructing a line perpendicular to a point off a lin Owith compass at P draw an arc above a O With compass at P draw an arc below a Owith compass at P draw an arc that intersects a in one place With compass at P draw an arc that intersects a in two places

The graph shows a relationship between the average number of hours 15 ninth graders spend studying per week and their grade point average Grade Point Average 4 0 3 0 2 0 1 00 0 10 2 4 6 Hours Spent Studying per Week Which equation best models this data set O 10 y 0 281 1 2 O y 1 22 0 28 y 0 28 1 2 y 1 2 0 28 8 x

What do you get when you cross a bunny and some cheese Find the slope between the following set of points The answer to each problem will match a letter that will allow you to figure out the joke 1 4 7 and 6 11 2 2 4 and 3 2 3 5 8 and 2 4 4 6 5 and 0 5 5 3 12 and 8 7 6 7 0 and 1 4 7 9 3 and 9 7 8 2 15 and 20 3 9 1 1 and 15 4 10 34 12 and 56 23 3 o 5 9 10 9 1 10 9 9 H 5 11 S T 4 1 4 A 0 V 11 2 O 5 R L 2 1 2 1 6 B T Undefined N 23 E 3 16 4 3 7 4

4n 176 0 19 4n 4n START 26 Find mzC E 136 136 Find the value of b 76 64 62 440 19 Tind the value of x 16 3x 4y 1 16 4 y 60 3x 12 3 3 4 6 7 Find the value of p 2p 49 3x 4 5K 124 28 Find the value of h 130 56 59 4 9 50 116 2h find the value of g g 7 15 h 8 177 10 6 65 9 8 g 7 22 Find the value of y 25 3x 6 2 Find the value of f 72 f 30 er 5 89 3 find the value of k 18 3 6k k 10 51 9 Find mzC 119 x 187 479 61 194 119 119 669 TO FINISH 28F 611 x OMISSCRAFTYMATHIEACE

Consider the figure where line segment MN is parallel to line segment PQ M P 1 4 2 3 5 N Q Which statement must be true Since m 1 m 2 m 3 180 m 1 m 4 and m 3 180 m 1 m 4 and m 3 m25 we can prove tha m 4 m 2 m 5 180 Since m 1 m 2 m 3 180 m 1 m 5 and m 3 m 4 we can prove that m 5 m 2 m 4 180 Since m 1 m 2 m 3 360 m 1 m 4 and m 3 m 5 we can prove that m 4 m 2 m 5 360 Since m 1 m 2 m 3 360 m 1 m 5 and m 3 m 4 we can prove that m 5 m 2 m 4 360

Use the graph to write an equation of the line Interpret the slope Tree height feet The height increases feet each year The height Increases 1 foot every 1 5 years Tree Growth 2 Age years 4 X The height increases 1 5 feet each y The height Increases 3 feet every 24 05

Part A The number of cubic feet of water y in a pool hours after the water starts flowing into the pool is a linear function The points 40 3000 and 60 4000 lie the line of the function Calculate the slope of the line Part B What does the slope of the line represent in Part A Explain in your own words and use complete sentences Part C Explain how the slope formula is related to the definition of slope Use complete sentences

Challenge Find the value of x for which r s Then find m 1 and m22 m 1 70 2x m 2 81 3x The value of x for which r s is The figure is not to scale

Alan buys cheese from the local farmer s market The graph below shows the cheese cost in cents versus its weight in ounces Use the graph to answer the questions Cost cents 280 245 210 175 140 105 70 35 0 Weight ounces a What is the slope of the line 0 Y 8 08 X

29 Determine if the graph represents a polynomial function If it is a polynomial function then determine the number of turning points and the least degree possible This is not a polynomial Lines are not polynomials There are no turning points This graph is not a polynomial This is a piecewise defined function that is constructed with two lines rays Where the lines are connected there is a CUSP point polynomials are represented by graphs with smooth curves Yes this graph represents a polynomial This is a piecewise defined function that is constructed with two lines rays There is only one turning point as each line is a polynomial of degree one

Tristan is studying the relationship between reaction time in seconds to the score achieved in a computer game Reaction time s X 0 210 0 230 0 245 0 199 0 211 0 231 0 278 0 291 0 222 Score y 1987 1898 1776 1990 2001 1811 1652 1432 1999 What is the gradient for the line of best fit Give your answer rounded to the nearest

Brianna s math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit What does the line s y intercept represent

From 1983 to 2003, the number B of federally insured banks could be approximated by B(t) = 322.6t+13787 where t is the year and t=0 corresponds to 1983. How many federally insured banks were there in 1988? Find the slope of the graph of B. Interpret this slope as a rate of change. Choose the correct answer below. The number of banks increased by 12174 banks per year The number of banks decreased by 322.6 banks per year The number of banks increased by 322.6 banks per year The number of banks decreased by 13787 banks per year The number of banks decreased by 12174 banks per year The number of banks increased by 13787 banks per year Find the y-intercept of the graph of B. The y-intercept is Interpret the y-intercept. Choose the correct answer below. The y-intercept is the maximum number of banks allowed in the country The y-intercept is the number of banks in 1983 The y-intercept is the minimum number of banks allowed in the country The y-intercept is the number of banks in 1988 The y-intercept is the number of banks in 2003

Find the functions which are parallel. I. 3x + 5y = 9 II. 3x + 8y = 12 III. 3x + 9 = -5y IV. 27x - 45y = 1 I and IV I and III II and III

Write the equation of the straight line passing through the point (5, 2) and having a slope of 1/2. y =1/2(x-1) y=2(x-2) y=1/2(x + 1)

Write the equation of the line that passes through the point (-8, 6) and has a slope of 4. y=4x-26 y=-4x-26 y = -4x+26

Write the slope-intercept form of the equation of the line with a slope of 2 and passing through the point (-4,-5). y=2x+3 y=-2x+3 y=2x-3

Determine the equation of the straight line with a slope 2 and passing through the point (1, 5). y=2x+3 y=10x-9 y=6x +15

Find the equation of the line passing through the points (2, 5) and (6, 1). y-x=7 y+x=-7 y+x=7

Determine the equation of the line, in y = mx+b form, perpendicular to 4x - 3y = 0 containing the point (-1, 2).

Graph the linear function by finding x- and y-intercepts. Then write the equation using function notation.. 2x - 4y= -4

Graph each of the lines in the following system to find the solution. y = -2x + 6 y=-3x+9

On the axes below, draw the graph of the function f(x) == -4x + 6.

The graph of a line in the xy-plane has slope 2 and contains the point (1,8). The graph of a second line passes through the points (1, 2) and (2, 1). If the two lines intersect at the point (a, b), what is the value of a + b? 4 3 -1 -4

Find an equation for the line perpendicular to 3x+6y= 54 and goes through the point (1, 3). Write your answer in the form y = mx + b.

Determine the solution to the system of equations below. 5x+6y=-44 -7x-7y= 49 Select the correct answer below: (2,-9) (8,-14) no solutions infinitely many solutions

What are the magnitude and direction of w = <-10, -12>? Round your answer to the thousandths place. ||w|| = 6.325; θ = 39.806° ||w|| = 14.422; θ= 219.806° ||w|| = 14.560; θ = 205.346° ||w|| = 15.620; θ= 230.194°

A line passes through the point (-3,-9) and has a slope of 9. Write an equation in point-slope form for this line.

Find an equation of the tangent line to f(x) = ex + 7x at the point (0, 1). Write your final answer in the form y = mx + b.

Determine the Angle Pair Types that are CONGRUENT when two parallel lines are cut by a transversal. (Select ALL that apply) * Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Same-Side Interior Angles Linear Pair Vertical Angles

Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation Slope = 5, passing through (-6,6) Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. (Use integers or simplified fractions for any numbers in the equation.)

Find the slope using the formula: 2-y1 / x2-x1 Plug in your slope and ONE of your coordinates (doesn't matter which) into the intercept form: y = mx +b Solve for b (your y-intercept) Write your formula into slope intercept form: y = mx + b

Graph the image of A(1,-3) after the described glide reflection. Then determine the coordinate of the image (A'). Translation: (x,y) → (x,y+2) Reflection: in the y-axis

Create a line that is parallel to AB and passes through point C. You can use the tools available in GeoGebra to create parallel lines for this construction. Take a screenshot of your results, and paste it below.