A construction crew is extending the length of the center line on a highway. The length of the center line starts out as 6 meters long, which is represented on a coordinate plane as the (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.
y= ? x+ ?
To determine the equation that represents the relationship between x (the number of minutes spent working) and y (the length of the line), we need to find the slope (m) and the y-intercept (b).
The slope can be found using the formula:
m = (change in y) / (change in x)
m = (17 - 6) / (20 - 0)
m = 11 / 20
The equation for the line is in the form y = mx + b, where m is the slope. Now, we need to find the y-intercept.
Using the point (0, 6), we can plug in the values of x and y into the equation and solve for b:
6 = (11/20)(0) + b
6 = b
Therefore, the equation that represents the relationship between x and y is:
y = (11/20)x + 6