Straight lines Questions and Answers

The coordinates of point A are (-1,-7) and the coordinate3s of point B are (5,2).L, is the line which passes through A and B. a) Find the equation of L₁. Point M is the midpoint of AB. The line L₂ is perpendicular to L₁ and passes through M. b) Find the equation of L₂.

Write the equation of the line, with the given Slope = 4, through (-4,7)

Graph this line using the slope and y-inter y = 8x - 7 Click to select points on the graph.

You work in an electronics store. You earn a fixed amount of $35 per day, plus a 15% bonus on the merchandise you sell. Write an equation that models the amount y (in dollars) you earn for selling x dollars of merchandise in one day. Graph the equation.

Find an equation of the horizontal line through (2, -9). The equation is (Type your answer in standard form.)

Find an equation perpendicular to y = 1 and passing through (6,-1). The equation is (Type your answer in standard form.)

Find an equation of the line with the slope m = 1/3 that passes through the point (-4,0). Write the equation in the form Ax+By=C. Choose the correct answer below. A. 4x+y=-3 B. 3x+y=4 C. x+3y=-4 D. 4x+y=3

Determine if the equations represent parallel lines, perpendicular lines, or neither. 1₁:3x=6 1₂:3=x The lines are neither parallel nor perpendicular perpendicular neither parallel nor perpendicular parallel X

Write an equation of the line with the given slope, m, and y-intercept (0,b). m = -3, b = -1/5

Graph using the x- and y-intercepts. y = 3x +3 Use the graphing tool to graph the linear equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Graph the linear equation. 4x=4y

Use the slope-intercept form to graph the equation x =(3/5)y

The point P(4, 27) lies on the curve y=x²+x+7. If Q is the point (x, x² + x + 7), find the slope of the secant line PQ for the following values of z. If z = 4.1, the slope of PQ is: and if = 4.01, the slope of PQ is: and if z = 3.9, the slope of PQ is: and if r = 3.99, the slope of PQ is: Based on the above results, guess the slope of the tangent line to the curve at P(4, 27).

Find an equation of the line with the slope m = - 8 that passes through the point (-2,-4). Write the equation in the form Ax+By = C. Choose the correct answer below. A. 20x + y = 8 B. 8x+y=20 C. 8x + y = -20 D. 20x + y = -8.

Find an equation of the line through the pair of points. Write the equation in the form Ax+By = C. (-7,3) and (8,-5) A. - 10x + 13y = 15 B. 8x - 15y = 11 c. 10x-13y = 15 D.-8x-15y = 11

Consider the piecewise linear function given by the formula f(x)=(2-3x tx-2 -1≤x≤l 1<x<3 . Determine the function's domain and range. Draw a graph of the function to fully justify your answer. Use tables on your calculator to help graph.

Let m₁ and m2 represent the slopes of two lines. Determine if the lines are parallel, perpendicular, or neither. m₁ = 1, m₂= 5/5 The lines are (Choose one)parallel perpendicular/neither parallel nor perpendicular

Consider the line with the equation: y = -4x-17 Give the equation of the line parallel to Line 1 which passes through (10, 4) : Give the equation of the line perpendicular to Line 1 which passes through (10, 4):

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Alexa is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.25. Alexa spent $22.50 altogether on 14 games and rides. Graphically solve a system of equations in order to determine the number of games Alexa played, x, and the number of rides Alexa went on, y.

The coordinates of the endpoints of KL are K(-9, 11) and L(15, -7). Point M is on KL and divides it into two parts such that the ratio of the lengths is 1:2. What are the two possible locations of M? (-5, 8) (8,-2) (-1, 5) (12,-5) (3, 2) (14, -6) (7, -1)

From the multiple choice, choose ALL that are true about vertical angles. They can be adjacent They can form a linear pair They always add to 180 They are always congruent They always add to 90

Find the slope of the graph of 7(x) = 13 – eª at the point where r(x) crosses the x-axis. The slope is = Find the equation of the line tangent to the curve at this point. y = Find the equation of the line perpendicular to the tangent line at this point. (This is called the normal line.) y =

For a and b, write an equation in slope-intercept form that meets the given criteria. a. A negative slope and passes through the origin b. Slopes upward from left to right and has a y-intercept below the x-axis.

Find an equation for the line perpendicular to the line 9x - 4y = 5 having the same y-intercept as 5x + 3y = 2.

A line has this equation: y=-x-2 Write an equation for the parallel line that goes through (3, 7).

An ostrich can run at a speed of 45 miles per hour. a) Copy and complete the following table to show the distances an ostrich can run in various times. Time in hours 0 1 2 3 4 Distance in miles 0 b) How does the distance vary with respect to time? c) Write a formula for this function, letting d represent the distance and t represent the time.

Without graphing, decide. a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point? b. How many solutions does the system have? 3x + y = 0 3y = 6 - 9x a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point? lines intersecting at a single point identical lines parallel lines

Your above-ground pool has sprung a leak, and you do not have a way to fix it. At 12 noon, the water in the pool is 5 feet deep (in other words, the water level is 5 feet above the ground). You are not sure how quickly the pool level is falling, so you check again after 40 minutes and see that the height of the water level is now 4 feet. You notice that there is a relationship between the time that has passed to the height of the water level in the pool. (a) If you assume the height of the water level is decreasing at a constant rate, what will be the height of the water level at 1 p.m.? (b) Write a linear function, h, that relates the time past noon, t, in minutes, and the height of the water level in the pool, h(t), in feet. (c) Explain the meaning of the rate of change of function h. (d) Evaluate h(75), and explain its meaning in the context of time passed and height of the water level. (e) At what time, t, will h(t)=0.5? What does your solution mean in the context of the problem? (f) When you check the pool at 3 p.m., the height of the water level is approximately 1 foot, 4 inches. What conclusions can you draw?

Consider the line y=7/9x+6. Find the equation of the line that is perpendicular to this line and passes through the point (-7, -2). Find the equation of the line that is parallel to this line and passes through the point (-7, -2).

Today, there were 2 members absent from the band. The present members folded 25 programs each, for a total of 525 programs. What question does the equation 525 = 25(x - 2) help answer? Choose 1 answer: A How many programs did each member fold? B How many programs would the members fold if no one were absent? C How many members are in the band when no one is absent?

At a particular restaurant, each mini hotdog has 100 calories and each chicken wing has 50 calories. A combination meal with chicken wings and mini hotdogs is shown to have 600 total calories and twice as many chicken wings as there are mini hotdogs. Graphically solve a system of equations in order to determine the number of mini hotdogs in the combination meal, x, and the number of chicken wings in the combination meal, y.

a line containing (8, 16) and perpendicular to y = 2x + 12

Tiffany started a doggie daycare where she offered a variety of services, including grooming. She charges an hourly rate of $9 and a fee for each service. Fluffy's human paid $58 for her 3 hour stay. Complete the function for a visit of x hours which includes grooming. Express the function in slope-intercept form. G(X)= Answer:

A dilation centered at the origin is applied to the line y = 3x + 5. What is true about the image of the line? O It is the same line. O It is another line parallel to y = 3x + 5. O The image is not a line. O The question cannot be answered without knowing the scale factor.

Gabriella expects to earn $50 in tips during her shift as a waitress today. In addition to tips, she earns $8.00 an hour. If she wants to make at least $114 today, how many hours must she work at a minimum?

In the year 1999, the surface elevation of Lake Powell was 3821 feet above sea level. In the year 2007, the surface elevation of Lake Powell was 3202.6 feet above sea level. Interpret the rate of change in this situation. The surface elevation of Lake Powell is ... at a rate of ...

An airplane begins a flight with a total of 39.3 gal of fuel stored in two separate wing tanks. During the flight, 25.3% of the fuel in one tank is used, and in the other tank 34.2% of the fuel is used. If the total fuel used is 12.1 gal, the amounts x and y available in each tank before flight can be found by solving the system of equations which is below. x+y=39.3 0.253x+0.342y = 12.1 Find x and y.

A company that packages cold cuts needs to transport the packaged meat to the supermarket. It will cost $1,200 to rent a truck, and it will cost an additional $100 for every 50 pounds transported. Which equation represents the transport cost for every 50 pounds of cold cuts transported? A y=1,200 - 100x B. y=1,200 + 100x C. y=1,200x+100 D. y=100x-1,200

A new car was purchased for $14,600, and 4 years later it was worth $6,600. Assume that the depreciation in value is given by a linear equation. Find the value of the car at the end of 5 years A. $12,600 B. $4,600 C. $8,000 D. $20,600

The intersection of the planes 3x+2y+5z = 22 and 2x+y+3z = 13 is a line, one of whose points is (1, 2, 3). Find another point on this line. Once you have found a second point, write the parametric description of all the points on the line.

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 a hours for her to complete.

Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (-4,-2); 2x-9y=5

A taxi driver buys a new car for $50,000. The car will have a scrap value of $10,000 after 8 years. Using the straight-line depreciation method, find the value of the car after 4 years. (A) $10,000 (B) $13,000 (C) $15,000 (D) $25,000 (E) $30,000

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through (3,12) and (0,3) The slope-intercept form of the line is y= (Simplify your answer. Use integers or fractions for any numbers in the equation. Do not factor.)

Classify the pair of equations. y=-x+6 y=-x-11 Use this space to write down notes or work through problems. Your teacher will see what you wrote. Your answer Parallel lines Perpendicular lines Neither

A linear equation is given in standard form: 4x + 5y = 20. Find the x-intercept: Find the y-intercept: Rewrite the given equation in slope intercept form:

Find three integer or decimal solutions to the following equation, and then graph the solution set. y = 3x - 2 (_________), (__________), (____,____),

Give the equation of the line passing through the points (-3/11,2/3),(-3/11,7). The equation of the line is:

The equation of the line that goes through the point (6, 4) and is parallel to the line 4x + 3y = 2 can be written in the form y = mx + b where m is: and where b is: