Final answer:
We found the points of intersection for the country road and the state highways by substituting x=0 to find the y-intercept and y=0 to find the x-intercept, yielding the points (0, 11.5) and approximately (15.33, 0) respectively.
Step-by-step explanation:
The question pertains to the intersection of a country road with two state highways, given by their respective equations. The road is defined by the equation -0.75x + 11.5, and it intersects the state highways along the x=0 (y-axis) and y=0 (x-axis). To find the points of intersection, we can substitute x=0 into the country road's equation to find the y-intercept, and y=0 to find the x-intercept.
For x=0 (y-axis), the country road equation becomes -0.75(0) + 11.5, which simplifies to y = 11.5. Therefore, the road intersects the y-axis at the point (0, 11.5).
For y=0 (x-axis), we set the equation -0.75x + 11.5 to 0 and solve for x:
0 = -0.75x + 11.5
0.75x = 11.5
x = 11.5 / 0.75
x = 15.33 (approximate to two decimal places).
So, the road intersects the x-axis at approximately (15.33, 0).