The equation that represents the relationship between x and y is [tex]y=\frac{11}{20}x+6[/tex]
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,
[tex]y-y_1=m(x-x_1)[/tex]
First, we shall determine the slope using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the coordinates [tex](0,6)[/tex] and [tex](20,17)[/tex], we get,
[tex]m=\frac{17-6}{20-0}[/tex]
[tex]m=\frac{11}{20}[/tex]
Now, we shall substitute the slope [tex]m=\frac{11}{20}[/tex] and the coordinate [tex](0,6)[/tex] in the formula [tex]y-y_1=m(x-x_1)[/tex], we have,
[tex]y-6=\frac{11}{20}(x-0)[/tex]
Simplifying, we get,
[tex]y-6=\frac{11}{20}x[/tex]
[tex]y=\frac{11}{20}x+6[/tex]
Thus, the equation that represents the relationship between x and y is [tex]y=\frac{11}{20}x+6[/tex]
