Perpendicular lines have opposite and inverse slopes, then if the first line has a slope "m1" the slope of the second line "m2" can be calculated by means of the following formula:
[tex]m2=-\frac{1}{m1}[/tex]
In order to find the slope of the first line (the path of the ball after being hitten by Pedro), we need to find two points (x1, y1) and (x2, y2)where it goes through, so we can use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
As you can see in the graph, this line passes through the points (0, 0) and (2, 8). By replacing (0,0) and (2, 8) into the above formula, we get:
[tex]m1=\frac{8-0}{2-0}=\frac{8}{2}=4[/tex]
Then, the slope of the second line would be:
[tex]m2=-\frac{1}{m1}=-\frac{1}{4}[/tex]
Now that we know the slope of second the line we can formulate its slope-intercept equation, the slope-intercept equation is given like this:
y = mx + b
Where m is the slope and b is the y-intercept.
By replacing -1/4 for m, we get:
[tex]y=-\frac{1}{4}x+b[/tex]
And we know that the line passes through the first base, located at (2, 0), by replacing 2 for x and 0 for y into the above equation we can solve for b to get:
[tex]\begin{gathered} y=-\frac{1}{4}x+b \\ 0=-\frac{1}{4}\times2+b \\ 0=-\frac{1}{2}+b \\ \frac{1}{2}=b \\ b=\frac{1}{2} \\ b=0.5 \end{gathered}[/tex]
By replacing 0.5 into the equation of the line we get:
[tex]y=-\frac{1}{4}x+0.5[/tex]
Then, option E is the correct answer
