the equation for line t can be written as y = 4x - 8. line u, which is perpendicular to line t, includes the…

Explanation:

Step1: Find the slope of line u

The slope of line t is 4. For two perpendicular lines, the product of their slopes is - 1. Let the slope of line u be $m$. Then $4m=-1$, so $m =-\frac{1}{4}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(8,8)$ and $m =-\frac{1}{4}$. Substituting these values, we get $y - 8=-\frac{1}{4}(x - 8)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 8=-\frac{1}{4}x+2$. Then add 8 to both sides of the equation: $y=-\frac{1}{4}x + 10$.

Answer:

$y=-\frac{1}{4}x + 10$