The equation for line t can be written as y=4x- 8 . Line u, which is perpendicular to line t, includes the point (8,8) . What is the equation of line u? Write the equation in tercept form . Write the numbers ; in the equation as simplified proper fractions , improper fractions, or integers. square

To find the equation of line u, we need to determine its slope and y-intercept.<br /><br />Step 1: Find the slope of line t.<br />The equation of line t is given as $y = 4x - 8$. The slope of a line in the form $y = mx + b$ is represented by the coefficient of x, which is 4 in this case.<br /><br />Step 2: Determine the slope of line u.<br />Since line u is perpendicular to line t, the slopes of line u and line t are negative reciprocals of each other. Therefore, the slope of line u is $-\frac{1}{4}$.<br /><br />Step 3: Use the point-slope form to find the equation of line u.<br />The point-slope form of a line is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and m is the slope. We are given that line u passes through the point $(8, 8)$, so we can substitute these values into the point-slope form:<br /><br />$y - 8 = -\frac{1}{4}(x - 8)$<br /><br />Step 4: Simplify the equation.<br />To write the equation in intercept form, we need to solve for y:<br /><br />$y - 8 = -\frac{1}{4}x + 2$<br /><br />$y = -\frac{1}{4}x + 10$<br /><br />Therefore, the equation of line u in intercept form is $y = -\frac{1}{4}x + 10$.