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 (1, 5). Find the equation of the location of the second street in standard form.

Answer 1

The equation of the location of the second street in standard form is; x + y = 2

Equation of a Line

The image of the line graph showing the two street points has been attached.

General formula for equation of line in slope intercept form is;

y = mx + c

Where;

• m is the slope of the line
• c is the y-intercept

Let us find the slope:

If we are given two points with the coordinates (x, y), then the slope is given by;

m =  change in y/change in x.

We are told that the equation of the street is parallel to the equation of the line in the graph and this implies that they have the same slope.

Thus, from the graph the coordinates of two sample points are: (-1, 2) and (0, 1).

Thus slope is;

m = (1 - 2)/(0 - (-1))

m = -1

From the graph the second street point is at -2, 4 and so let us find the y-intercept of the line passing through this point from;

4 = -1(-2) + c

4 = 2 + c

c = 4 - 2

c = 2

Therefore, the equation of the line is;

y = -x + 2

In standard form, the equation is;

x + y = 2

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