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.
To find the equation that represents the relationship between x and y, we can use the slope-intercept form of a linear equation: y = mx + b. In this form, m represents the slope of the line and b represents the y-intercept.
Given that the length of the line starts at 6 meters (0,6) and increases to 17 meters (20,17), we can use these two points to find the slope (m).
The formula for calculating slope is: m = (y2 - y1) / (x2 - x1)
Using the points (0,6) and (20,17), we have:
m = (17 - 6) / (20 - 0)
m = 11 / 20
Now that we have the slope (m), we can substitute it into the slope-intercept form of a linear equation to find b:
y = (11/20)x + b
Now we need to find the value of b. We can use one of the given points, such as (0,6):
6 = (11/20)(0) + b
6 = b
Thus, the equation that represents the relationship between x, the number of minutes spent working, and y, the length of the line, in meters is:
y = (11/20)x + 6