Straight lines Questions and Answers

Consider the graphs of the equations below. y = 3x + 5 (y-7)= 2(x - 1) -12x + 3y = 15 -y = 6x - 5 Select the true statement. A. All four lines cross the y-axis at (0,5). B. All four lines have a positive x-intercept. C. All four lines have a negative x-intercept. D. All four lines cross the x-axis at (5,0).

Write an equation that models the linear situation: A baby grows about an inch every month for the first year. She was born a foot and a half long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: m = age of the baby (months) L(m) = length of the baby (inches) Equation:

Polly and Olivia just had business cards made. Polly's printing company charged a one-time setup fee of $10 and then $7 per box of cards. Olivia, meanwhile, ordered hers online. They cost $8 per box. There was no setup fee, but she had to pay $5 to have her order shipped to her house. By coincidence, Polly and Olivia ended up spending the same amount on their business cards. How many boxes of business cards did each buy? Write a system of equations, graph them, and type the solution.

The two points (-3, 6) and (6, 0) are plotted on the grid below. (a) Find an equation, in y=mx+b) form, for the line passing through these two points. Use of the grid is optional. b) Does the point (30, -16) lie on this line? Justify.

A cashier has a total of 48 bills in her cash drawer. There are only $20 bills and $5 bills in her drawer. The value of the bills is $465. How many $20 bills are in the drawer? 31 $20 bills 17 $20 bills 15 $20 bills 33 $20 bills

Find an equation of the line parallel to 10x-y=9 and passing through (3,8), Express the equation in standard form. Which of the following is the equation of a line parallel to 10x-y=9 and passing through (3,8)? A. x+10y=24 B. 10x-y=24 C. 10x-y=36 D. x+10y=36

Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are (a, b) and she reflects the figure over the line y = x. What are the coordinates of the image D'? (1)(a, b) (2)(b, a) (3)(-a, b) (4)(-b, -a)

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?

Graph the linear equation. f(x) = -3x + 4 Use the graphing tool to graph the linear equation.

Use function notation to write the equation of the line with the given slope and y-intercept. Slope -5; y-intercept (0.3) The equation is f(x)=_________

Graph the linear equation; f(x) = 3x Use the graphing tool to graph the equation.

In the coordinate plane below, plot the three points corresponding to the values x = -1, x = 0, and a = 1 ,in the equation y = - +5

Find an equation of the line through (3,7) and parallel to y = 4x - 7. Write the equation using function notation.

A video on Tiktok was posted. on day 4 there was 6 views on day 10 there was 26 views make a point slope or slap-intercept equation with given data. use the equation you have the find how many views on day 0. Do you think this data is accurate.

Graph the linear equation. f(x) = 3x

Find an equation of the line passing through the given points. Use function notation to write the equation (-8, -2) and (-12, -1).

Do the points (0, -7), (-3,- 22) and (2,3) lie on the same line? Explain why or why not. (Hint: Find the slopes between the points). Do the three points lie on the same line? (A) Yes, because the slopes are not the same. (B) No, because the slopes are the same. (C) Yes, because the slopes are the same. (D) No, because the slopes are not the same.

Write an equation of the line using function notation. Horizontal; through (0.-4) The equation of the line is f(x) = _____

Graph the linear equation. f(x)=(1/2)x +1

For each function below, identify the Slope, horizontal-intercept and vertical-intercept Write your numerical answers as whole numbers or reduced fractions. Write your intercepts as ordered pairs. If a slope or intercept Does Not Exist, write DNE Function Slope Vertical Intercept Horizontal Intercept y = 4x + 3 y = -8x + 7x y = 10x y = 2 x= -6

Assume that you don't know the commission rate, but you do know the actual amount of daily commission you earned and the total dollar value of the shoes you sold. Based on these values, you can derive a formula for the commission rate. Using the slope-intercept form of a line, write an equation to calculate the commission y, based on sales, x. Hint: The y-intercept will be zero since you get no commission if you have no sales.

Find the slope, y-intercept. Then use the slope and the y-intercept to find a second point for graphing the line. x+y=2 Slope = y-intercept:

A town's population increases at a constant rate. In 2012 the population was 50,903. By 2019 the population had increased to 103,753. Assume this trend continues. Predict the population in 2022. Identify the year in which the population will reach 191,000.

If the point (1,4) is on the graph of an equation, which statement must be true? A. There are solutions to the equation for the values x = 1 and x = 4. B. The values x = 4 and y = 1 make the equation true. C. The values x = 1 and y= 4 are the only values that make the equation true. D. The values x = 1 and y = 4 make the equation true.

Solve the given system of equations. x + y +9z = - 40 x + y + 4z = -15 x-7y-6z= 11 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is (()}. (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

What is the slope of a line that is parallel to the line whose equation is 5y + 2x = 12? A. 2/5 B. -5/2 C. 5/2 D. -2/5

Line c has an equation of y = -1/3x - 4. Line d is perpendicular to line c and passes through (-1, 3). What is the equation of line d? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Line t has an equation of y = -10x + 9. Line u includes the point (-1, 5) and is parallel to line t. What is the equation of line u? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Line r has an equation of y-3 = 5(x + 4). Line s includes the point (3, 10) and is parallel to line r. What is the equation of line s? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Write the equation of the line that is perpendicular to the line 5y = x-5 through the point (-1,0). Ay=-5x-5 B.y=1/5x+5 C .y=1/5x-5 D.y = -5x + 5

A parabola has a vertex at (2,5) and opens down, is reflected across the line y = x. What is the image of the vertex after the reflection? A. (5,2) B. (-2,-5) C. (2,-5) D. (-5,2)

The equation for line p can be written as y = =-4/7x + 7. Perpendicular to line p is line q, which passes through the point (8, 7). What is the equation of line q? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

The equation of line r is y =-2X/3- 3. Line s, which is parallel to line r, includes the point (8,-8). What is the equation of line s? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

A tennis club offers two payment options. Members can pay a monthly fee of $12 plus $7 per hour for court rental time. The second option has no monthly fee, but court time costs $8.50 per hour. Answer parts a through d. a. Write a linear function that models the total monthly costs for each option for x hours of court rental time. The linear function that models total monthly cost for the first payment option is f(x) = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression.)

A parallelogram must be a rectangle if it's diagonals: A. are congruent B. are perpendicular to each other C. bisect the angles in the parallelogram D. bisect each other

The equation for line k can be written as y = x - 8. Line / includes the point (-1, -7) and is perpendicular to line k. What is the equation of line /? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Suppose the least squares regression line for predicting weight (in pounds) from height (in inches) is given by Weight = -115 +3.6(Height). Which of the following statements is true based on the regression line? I. A person who is 61 inches tall will weigh 104.6 pounds. II. For each additional inch of height, weight will increase on average by 3.6 pounds. III. There is a strong positive linear relationship between height and weight. (A) I only (B) II only (C) III only (D) II and III only (E) I and II only

Find a slope that is parallel and one that is perpendicular to the given equation. y = 1/4 x + 3

Find the equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form. (-6,-5), m= 4 What is the slope-intercept form of the equation that passes through (-6, -5) and has a slope of 4?

Find the slope, x-intercept, and y-intercept for the line 5x - 4y - 6=0. The slope is The x-intercept value is The y-intercept value is Note: Your answers must be decimals.

Find the equation of the line, in slope-intercept form, that satisfies the given conditions. The graph is parallel to the graph of x + 2y = 8 and passes through the point whose coordinates are (-2,-4).

Patrick is given the following point and slope: Slope = -3 y-intercept = (0,6) He answers the following questions. Identify if he got each problem correct or Incorrect. If he answers a problem wrong, please do the problem correctly with explanation. 1) Write the equation for the line in Slope-Intercept Form y=-3x+6 2) What is the x-intercept of the line? The x-intercept of the line would be 6, because you are given (0,6) 3) Write the equation for the line in Standard Form -3x+y = 6 4) Using the point (1,3), write the equation for the line in point-slope form y-3 = -3(x-1)

equation of the line with the given slope, m, and y-intercept (0,b). m=6, b=5 The equation is Write an

What is this called: change in y over the change in x A) Formula to find the slope of a line B) Standard form c) Point Slope form D Slope-Intercept form

What is the slope of the line with the equation: y = 4x + 12 A 4 B 1/4 C -1/4 D -4

Find the slope of the line that passes through (10, -8) and (1, 12). 4/9 -20/9 9/4 20/9

Write the equation in point-slope form of the line that passes through the given point and has the given slope: (-2,-1); m= -3 A. y-1=3(2-1) B. y+2=-3(x+1) C. y+1 = -3 (x-2) D. y+1 = -3(x+2)

What is this called: y=mx+b A) Formula to find the slope of a line B) Point-Slope form c) Slope-Intercept form d) Standard form

What is the x-intercept for the equation: 3x + 8y = 24 (8,0) (0,3) (0,8) (3,0)

One line passes through the points (2, 1) and (5, 7). Another line passes through points (-3, 8) and (8,3). Are the lines parallel, perpendicular, or neither? Choose 1 answer: A. Parallel B. Perpendicular C. Neither