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.

what would the equation be please help me

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.

what would the equation be please help me

InsatiableSuffering · Answer

Simply find the derivative given the two points. Or in simpler terms, find the slope of the linear equation. We will be using y=mx+b to solve this one. So we know that our b value will be 6, as that's the initial value. The only part that's missing is the slope. In order to do so, simply follow the following formula:$$(y1-y2)/(x1-x2)$$
This allows us to find the slope, as slopes are rise/run, or the change in y values divided by the change in x values. So now just plug in the points to the equation. We have (0,6) and (20,17). So our equation would be:
$$(17-6)/(20-0)$$
Solving this, we find that the slope is 11/20. Therefore, the equation to the line is y=.55x+6.