Straight lines Questions and Answers

Consider a line L which passes through the point (-3, 10) and is perpendicular to the line with equation y = 4x + 5. (a) Find an equation for L. (b) Find the angle of inclination of L. Write your answer in degrees, correct to two decimal places.

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 15 HOF of water is $39.57, and the cost for using 33 HOF is $71.07. What is the cost for using 19 HOF of water?

What is the image of P(3, 4) reflected across the line x = -1? A. (-5,4) B. (-3, 4) C. (3, -4) D. (5, -4)

Find the x-intercept and y-intercept of the graph of 3x - 2y = -6. Then graph.

The equation of line R is 6x + 5y = 3, and the equation of line S is 5x - 6y=0. Which statement about the two line are true? Lines R and S are parallel. Lines R and S are perpendicular. Lines R and S have the same x - intercept. None of the above.

Write the equation in the form y=mx+b. Then, using your calculator, graph the line in the window [-10,10] by [-10,10]. 2x + 5y = 10 Write 2x + 5y = 10 in the form y = mx + b. y=

The coordinates of the vertices of AFGH are F(2,-1), G(-2,-2), and H(-4,3). Graph AFGH and its reflection over the line y = x - 3.

Find the equation of the line that contains the point (-2,-1) and has a slope that is undefined. Express the equation using either the general form or the slope-intercept form of the equation of a line. The equation of the line is (Type an equation.)

(a) Write the equation in slope-intercept form, and determine the slope and y-intercept. (b) Graph the equation using the slope and y-intercept. -4x=-2y+8 The slope is The y-intercept is (0. The equation written in slope-intercept form is

Find the y-intercept and the slope of the line. -2x-y=3 Write your answers in simplest form.

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Perpendicular to the line x-4y= -3; containing the point (0,4)

What is the slope of a line that goes through the points (6.-9) & (14,12). Reduce if possible. 8/21 8/3 21/8 7/4

Which equation in point-slope form is written correctly for a line that is parallel to y=4x+3 and goes through the point (-4,8)? y-8=4(x+4) y+8=4(x+4) y+8=4(x-4) y-8=4x(x+4)

If you drive 170 miles and have 14 gallons of gas remaining in your tank. Then you continue driving, and calculate that after driving 230 miles you have 11 gallons left.

Use intercepts to graph the equation. 2x+4y+8=0

The key features of linear functions include: To find the To find the This the average of a line, set y equal to of a line, set x equal to Slope-Intercept Form of a Line: Standard form of a line: of the line, and solve. and solve. If you need to find the equation of a line, the following equations may be useful: Slope of a Line =

Rewrite the equation 6x-2y-2=0 in slope-intercept form. Give the slope and y-intercept. Use the slope and y-intercept to graph the linear function.

Find the equation of the line that contains the point (-1,7) and has a slope that is undefined. Express the equation using either the general form or the slope-intercept form of the equation of a line.

Tangents are drawn to a unit circle centre at origin from every point on the line 2x + y = 4, then (i) Prove that chord of contact passes through a fixed point. (ii) Find equation to the locus of the middle point of chord of contact.

The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. a. Find the cost function C when "x" energy drinks are manufactured. C(x) = Write your answer in slope-intercept form. b. Find the revenue function R when "x" drinks are sold. R(x) = Write your answer in slope-intercept form. c. Graph both your Revenue and Cost functions on the graph below that shows the break-even point.

Find the equation of a line that is perpendicular to the line x = 1 and contains the point (6,2). The equation of the perpendicular line is (Type an equation.)

Select the answer that best completes the given statement. The slope, m, of a line through the distinct points (x1.y1) and (x2.y2) is given by the formula m =

a. Rewrite the equation 3x +y -4 = 0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is. .....

a. Rewrite the equation 4x - 2y – 6=0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function.

Use intercepts to graph the equation. 2x-2y+2=0

Determine the x- and y-intercepts for the given function. Write your answer as an ordered pair. h(x)=6x-36 If there is more than one answer, separate your answers with commas. Select "None" if appropriate. Part 1 of 2 x-intercept(s): Part 2 of 2 y-intercept(s): (0,0) 0.0.... None X Ś (0,0) DO.... None X S

Fill in the blank below so that the resulting statement is true. If a line rises from left to right, the line has slope. If a line rises from left to right, the line has slope.

Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are parallel, perpendicular or neither. y-3x+7 Possible answers No Answers Chosen 3y-9x-12 ⠀ Parallel The slopes are: 1/2 and -1/2 -3x+6y=18 Neither parallel or perpendicular -3x-6y + 14 No Answers Chosen The Slopes are 3

Find the SLOPE of the line through the two points: ( – 8, 9) and (8, 7)

PRACTICE ANOTHER Calculate the exact slope m (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (0, 1) and (-) M=

Calculate the exact slope m (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (0, 0) and (1,7)

Write the equation of a line that is parallel to y = 0.6x + 3 and that passes through the point (-3,-5).

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. What was her speed? 0.1 mile per minute 0.5 mile per minute 5 miles per minute 10 miles per minute

7 More practice. Start with 5p+10x = 15. (a) What are the p-intercepts? (b) What are the x-intercepts? (c) Solve for p in terms of z. If you were to graph this with r on the horizontal axis, what would be the slope? (d) Solve for z in terms of p. If you were to graph this with p on the horizontal axis, what would be the slope?

Find an equation of a line that is tangent to the graph of f and parallel to the given line. Line Function f(x) = x³ 12x - y + 9 = 0 y II y = (smaller y-intercept) (larger y-intercept)

‒‒‒‒‒‒‒ Find the slope and y-intercept (if possible) of the line. (If an answer is undefined, enter UNDEFINED.) 5x - 9y = 27

The chart shows the cost of tuition at a certain state university. Model the data in the chart with a linear function, using the points (1,10073) and (3,11344). Predict the cost of college tuition in 2003-2004.

The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 cones. Use linear interpolation to estimate the demand at a price of $1.50 per cone.

The slope and a point on a line are given. Use this information to locate three additional points on the line. Slope 4; point (-6,1) Determine three points on the line with slope -4 and passing through (-6,1). A. (-2,0), (-10,2), (-14,3) B. (5,-7), (-3,-5), (-7,-4) C. (0,-2), (2,- 10), (3, -14) D. (-7,5), (-5,-3), (-4,-7)

If the lines 3x² +8xy-3y² = 0 and 3x² +8xy-3y² +2x-4y-1=0 from a quadrilateral ABCD. Then which of the following is/are true? The quadrilateral is a square One of the diagonal of the quadrilateral has equation 2x-4y-1=0 One of the vertex of the quadrilateral can be 3/10, -1/10 One of the side of quadrilateral has the equation as 3x-y-1=0

a. Rewrite the equation 16x-4y-8=0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is y=4x-2. (Simplify your answer. Use integers or fractions for any numbers in the equation.) b. The slope of the line is 4 and the y-intercept is -2 (Type integers or fractions.) c. Use the slope and the y-intercept to graph the line.

a. Rewrite the equation 8x-4y-4-0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is (Simplify your answer. Use integers or fractions for any numbers in the equation.) b. The slope of the line is and the y-intercept is (Type integers or fractions.) c. Use the slope and the y-intercept to graph the line.

If you are given a graph of a linear function, f(x) = mx + b is a way of symbolizing any linear function. a. Explain how you can determine m and b in the graph. b. Explain any effects that positive, negative and fractional values of m and b have on the graph.

Find the coordinates of the missing endpoint if M is the midpoint of AC A(5, 8) and M(-4,3) Find C(

a. Rewrite the given equation 7x+8y-56=0 slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is y=x+7. (Simplify your answer. Use integers or fractions for any numbers in the equation.) b. The slope of the equation of the line is and the y-intercept is (Type integers or fractions.)

Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is (Simplify your answer.) B. The slope is undefined. Indicate whether the line through the points rises, falls, is horizontal, or is vertical. A. The line rises from left to right. B. The line is horizontal. C. The line falls from left to right. D. The line is vertical.

Graph the line with the equation y = 4x - 1.

Use intercepts to graph the equation. 4x-3y-12=0 Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, useIt and another point to draw the line.

a. Rewrite the equation 9x-3y-3-0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is

Discuss whether a vertical line ever has a y-intercept. Choose the correct answer below. A. No vertical line has a y-intercept. B. Any vertical line except x = 0 never has a y-intercept. C. All vertical lines have a y-intercept.