Question

A contractor is building a new subdivision on the outside of a city. He has started work on the first street and is planning for the other streets to run in a direction parallel to the first. The second street will pass through (−2, 4). Find the equation of the location of the second street in standard form.

coordinate grid with a segment labeled Street 1 that extends between the points negative 5 comma 6 and three comma negative 2; a point labeled Street 2 is at negative 2 comma 4

2x + y = 2
x − y = 2
2x − y = 2
x + y = 2

Answer 1

Explanation:

A street parallel to Street 1 will have a line equation that has the same slope as Street 1. Lets find an equation for Street 1 in the form of y=mx+b, where m is the slope. We can then use that for Street 2.

Slope is Rise/Run

Take any two points on Street 1:

(-5,6) and (0,1) look good (easily read and zero's are always fun). Calculate the Rise and Run, going from (-5,6) to (0,1)

Rise = (1 - 6) = -5

Run = (0 - (-5)) = 5

Slope = Rise/Run = -5/5 or -1

The equation for Street 1 has a slope, m, of -1. We can now write:

Street 1: y = -1x + b

b is the y-intercept (the value of y when x is zero). Point (0,1) tells us that b = 1. We could also just enter any point on the line and solve for b:

y = -1x + b

6 = -1(-5) + b for (-5,6)

b = 1

The equation of the line for Street 1 is y = -x + 1.

Since Street 2 is parallel, it will have the same slope. We can write:

Street 2: y = -x + b

This looks the same as for Street 1, but the difference is that Street 2 must go through point (-2,4). This means b needs to be different. Find a value b that will move the line so that it intersects (-4,5).

Street 2: y = -x + b

4 = -(-2) + b for point (-2,4)

4 = 2 + b

b = 2

The equation for Street 2 is y = -x + 2

We'll rearrange to better match the answer options:

y = -x + 2

y + x = 2

Options

2x + y = 2

x − y = 2

2x − y = 2

x + y = 2 YES

See attached graph.