Question

A construction crew is extending the length of the center line on a highway. The length of the line starts out as 6 meters long, which is represented on a coordinate plane as the point (0,6). The crew works for 20 minutes and the line is now 17 meters long, which is represented as the point (20,17).
Complete the equation that represents the relationship between x, the number of minutes spent working, and y, the length of the line, in meters.

Answer 1

The equation that represents the relationship between x and y is $y=\frac{11}{20}x+6$

Explanation:

Given that a construction crew is extending the length of the center line on a highway.

The length of the line starts out as 6 meters long, which is represented on a coordinate plane as the point (0,6). The crew works for 20 minutes and the line is now 17 meters long, which is represented as the point (20,17).

Let x represents the number of minutes spent working.

Let y represents the length of the line in meters.

We need to determine the equation that represents the relationship between x and y.

The equation can be determined using the formula,

$y-y_1=m(x-x_1)$

First, we shall determine the slope using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the coordinates $(0,6)$ and $(20,17)$, we get,

$m=\frac{17-6}{20-0}$

$m=\frac{11}{20}$

Now, we shall substitute the slope $m=\frac{11}{20}$ and the coordinate $(0,6)$ in the formula $y-y_1=m(x-x_1)$, we have,

$y-6=\frac{11}{20}(x-0)$

Simplifying, we get,

$y-6=\frac{11}{20}x$

     $y=\frac{11}{20}x+6$

Thus, the equation that represents the relationship between x and y is $y=\frac{11}{20}x+6$