Question

A pair of linear equations is shown below:

y = -x + 1
y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)

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

That would be option D

The y intercepts are 1 and 4 and the slope are -1 and 2.

Answer 2

The correct option is D.

Explanation:

The given equations are

`y=-x+1`

`y=2x+4`

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

In equation (1),

`y=-x+1`

Here, m=-1 and b=1. It means the slope of the line is -1 and y-intercept is 1.

In equation (1),

`y=2x+4`

Here, m=2 and b=4. It means the slope of the line is 2 and y-intercept is 4.

The steps to solve the pair of equations graphically are:

Step 1: 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.

Step 2: Write the coordinates of the point of intersection of the two lines as the solution.

Therefore the correct option is D.