Straight lines Questions and Answers

Draw a AXYZ on a coordinate grid such that the slope of the line segment XY = 2/3. Draw the following transformations and determine if the following transformation will still have the same slope as the pre- image. Rotation of 180 degrees - O True O False

Find the ordered pair (x, y) that is a solution of the following system. -8x - y =5 -24x + 3y=33 Enter your answer as an ordered pair (x, y). If the system is inconsistent, enter Ø.

A line passes through the point (6, -7) and has a slope of 3/2. Write an equation in point-slope form for this line.

A line passes through the point (-8, 5) and has a slope of - Write an equation in point-slope form for this line.

9) The equation of a line L₁ is y = 1.5x + p. The point A(2,4) lies on L₁. a) Find the value of p. 433=28 3 tp A second line, L2, is perpendicular to L₁ and intersects L₁ at point A. b) Find the slope of L2. M=1 X c) Find the equation of L2. Give your answer in the form y = mx + b. x | Y = d) Write your answer to part (c) in the form ax + by + c = 0, where a, b, c, EZ.

Solve and check the linear equation. 2x-3=31 The solution set is ... (Simplify your answer.)

Carlota wrote the equation y + 1 = 2(x-3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her error.

Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once. 4x = 2y - 6 y = 2x + 3 4x = 2y-6 2x + 4 = y 4x = 2y - 6 y + 4x = 3 inconsistent consistent independent dependent

A line passes through the point (8,9) and has a slope of 5/4 Write an equation in point-slope form for this line.

Find the slope of the line containing the pair of points. (8,12) and (7,-2) The slope of the line is (Simplify your answer. Type an integer or a fraction.)

Find the equation of a line with the given information: f(-7) = -10 and f(7) = -1. Write your answer in point-slope form. If your answer is a vertical line, type your answer as x = #, and if your answer is a horizontal line, type your answer as y = #. Write your answer in slope-intercept form. If your answer is a vertical line, type your answer as x = #, and if your answer is a horizontal line, type your answer as y = #.

3. Answer all parts here, include all of your work and the Graph in your UPLOAD to receive full credit. Jenny sells cars at a dealership. She is guaranteed $2000 a month as long as she sells a minimum of 6 cars per month. She also earns $400 for every car she sells. a. Write the equation to help her calculate her monthly salary. b. Compute Jenny's monthly salary when she sells 6 cars. c. Compute Jenny's monthly salary when she sells 10 cars. d. Identify the slope. e. Draw the graph. Label the x and y axis. Plot the two points for selling 6 cars and 10 cars. Draw the line to include the y-intercept. Make sure all of your math work and this part is included in your Upload for full credit.

AABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image? A. A'(0, 3), B'(2, 3), C'(1, 1) B. A'(0, -3), B'(3,-2), C'(1,-1) C. A(-3,0), B'(-3,2), C'(-1, 1) D. A'(0, -3), B'(-2, -3), C'(-1,-1)

If two lines / and mare parallel, then a reflection along the line /followed by a reflection along the line m is the same as a OA) composition of rotations. B) translation. C) reflection. D) rotation.

Find the slope of the following line. - 9x - 7y = - 63 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

Write the equation of the line in slope-intercept form, y = mx + b. that passes through the points (3, 17) and (8, 24) (Round your answer to one decimal). y = 14 x y=1.4x + 12.8 y = 1.4 x -12.8 y = -1.4 x + 12.8

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x + y = 8 6x + 2y = 16 {(0,8)} {(5, -7)} {(x, y) | 3x+y=8}

Consider the equation and the following ordered pairs: (2, y) and (x,-3). 3x + 4y = 6 Step 2 of 2: Plot the resulting set of ordered pairs using your answers from Step 1.

Find an equation of the line containing the points (5, 7) and (3, 1). Find an equation of a line with a slope of 2/3 and having the point (3, 5) on the line.

Given that y varies directly with x, use the values specified to write a direct variation equation relating y to x. x = 3, y = -6

For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables). If it does, find the constant of variation and write it in simplest form. -2x = 5y + 8 Direct variation Not direct variation 2y = 12x Direct variation Not direct variation

Which one of the two equations has the same vertical or y-intercept as y= 5/4 x - 8/3? Explain/show how you know. y = -8/3 x + 6/5 x y = 6/5 x - 5/4

Write the equations of the lines that form the four sides of the right trapezoid with vertices at (-16, 8), (-16, -2), (6, -2), and (16, 8). line passing through (-16, 8) and (-16, -2) line passing through (-16, -2) and (6, -2) line passing through (6, -2) and (16, 8) line passing through (16, 8) and (-16, 8)

The point-slope form of the equation of a line is y - y₁ = m(x-x1), where m is the slope and (x₁, y₁) is a point on the line. Write the equation of the line in point-slope form perpendicular to the graph of y = ½X - 9 passing through the point (2, 7).

Given line segment AB with endpoints A(1, 14) and B(10, 4), state its image after the composition. (x, y) ⇒ (x-15, y + 7) (x, y) ⇒ (x+2, y - 13)

The points (w, 7) and (-3, 8) fall on a line with a slope of 1/6. What is the value of w?

Given line segment AB with endpoints A(1, 14) and B(10, 4), state its image after the composition. (x, y) (x-15, y + 7) (x, y) (x+2, y - 13)

In the USA, the shoe sizes for men are approximated by the equation 3f-s=24, where / represents the length of the foot in inches and s represents the shoe size. The average man's foot is 11.5 inches long. What is the average man's shoe size?

(1 pt) In May 1991, Car and Driver described a Jaguar that sold for 980,000 dollars. Suppose that at that price only 40 have been sold. If it is estimated that 400 could have been sold if the price had been 540,000 dollars. Assuming that the demand curve is a straight line, and that 540,000 dollars and 400 are the equilibrium price and quantity, find the consumer surplus at the equilibrium price. surplus = thousands of dollars

Windmill An architect is designing a new windmill with four sails. In her sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point Q, has coordinates (4, -6). She wants to make another sketch that shows the windmill after the sails have rotated 270° about their center of rotation. What would be the coordinates of Q'?

Fill in the blanks below. Find the slope of the line passing through the points (-6, -2) and (6, -2). slope: Find the slope of the line passing through the points (2, 2) and (-4, 2). slope:

Which of the following are the correct properties of slope? Check all that apply. A. Some lines have an undefined slope. B. If two lines have the same slope, then they are the same line. C. A steep line has negative slope. D. The slope of a line that moves up from left to right is positive. E. The slope of a line is always positive.

For a line passing through the point of intersection of angle bisectors of coordinate axes and parallel to line 3x - 5y + 17 = 0, which of the following is/are correct? Equation of line is 3x - 5y = 0 It passes through (5, 3) It passes through (-5, -3) It passes through (-3,-5)

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

Leslie and Ben are designing a neighborhood. They want the diagonals from the center of each lot to be perpendicular to one another. The center of the first lot is located at the coordinate (0,0). Another lot has been placed at (9,3), and a third is located at (6, -13). What is the equation of the line that goes through the third lot, and is perpendicular to the first two?

Suppose that the cost of a rental car is $65 for a week plus $0.15 per mile driven. An equation that represents the total weekly cost is y = 0.15z + 65, where is the number of miles driven. What is the total cost of the car if you travel 50 miles?

The student government is hosting a student carnival fundraiser. Students pay an admission fee, then can purchase tickets to pay for games or food. The tickets cost $1.50 each. Alexandra attends the carnival and purchases 14 tickets, spending $33.50 in total. Mackenzie attends and purchases 38 tickets, spending $69.50 in total. If y is total spending and is the number of tickets....

A phone company has a monthly cellular data plan where a customer pays a flat monthly fee and then a certain amount of money per megabyte (MB) of data used on the phone. If a customer uses 40 MB, the monthly cost will be $18.20. If the customer uses 100 MB, the monthly cost will be $23.00. Find a linear equation for the monthly cost of the data plan, C, as a function of , the number of MB used.

(a) Find the slope of the line through (-6,-9) and (-10,-33). (b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. A. The line through the points rises from left to right. B. The line is horizontal. C. The line is vertical. D. The line through the points falls from left to right.

In the xy plane, a line crosses the y axis at point (0, 4) and passes through point (6, 8). Which one of the following could be an equation of the line?

Line m and line k lie on the xy-coordinate plane, and line mis perpendicular to line k. Which of these statements could be true? Select all that apply. (A) Line m and line k intersect. (B) Line m and line k have the same slope. (C) The sum of the slopes of lines m and k is 0. (D) Line m creates an acute angle at the intersection with line k. (E) The product of the slopes of lines m and k is -1.

The line passing through which two ordered pairs would be perpendicular to the equation y = 4x - 1? A. (1, -3) and (2, 1) B. (-4, 7) and (-1,-5) C. (-8,-4) and (0, -2) D. (4, 2) and (8, 1)

The point P(9,-4) lies on the curve y = 4/(8 - x). (a) If Q is the point (x, 4/(8 - x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.

Part A: The number of cubic feet of water, y, in a pool x hours after the water starts flowing into the pool is a linear function. The points (40, 3000) and (60,4000) lie on 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.

Find an equation of the line tangent to the graph of f(x)= 3/x at (-6,-1/2) The equation of the tangent line is y =

Determine whether the pair of lines are parallel, perpendicular, or neither. 2x-5y +3=0 and 15y = 6x-1 The slope of the line with the equation 2x-5y +3=0 is__ (Type integers or simplified fractions.) The slope of the line with the equation 15y = 6x-1 is__ Since the slopes are the pair of lines are

A line passes through the point (-2, 4) and has a slope of 6. Write an equation in slope-intercept form for this line.