Question

A pair of linear equations is shown:

y = −x + 1
y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically?

A. On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and
y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and
y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and
y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Answer 1

Answer: the answer is D

Explanation:

Answer 2

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Explanation:

Each equation is in the slope-intercept form:

y = mx + b

in which m is the slope and b is the y-intercept.

__

Matching this form to the given equations, you find that ...

first equation: m = slope = -1; b = y-intercept = 1

second equation: m = slope = 2; b = y-intercept = 4

Comparing these values to those in the answer choices makes it clear which one is correct (see above).