40 Line u has an equation of y+6=(3)/(2)(x-6) Line v is perpendicular to line u and passes through (2,-1) What is the equation of line v? (1) Write the equation in slope-intercept form Write the numbers in the equation as simplified proper fractions,improper fractions, or integers. square

To find the equation of line v, we first need to find the slope of line u. We can do this by rearranging the equation of line u into slope-intercept form (y = mx + b), where m is the slope.<br /><br />Given: $y + 6 = \frac{3}{2}(x - 6)$<br /><br />Step 1: Distribute the $\frac{3}{2}$ on the right side of the equation:<br />$y + 6 = \frac{3}{2}x - 9$<br /><br />Step 2: Subtract 6 from both sides to isolate y:<br />$y = \frac{3}{2}x - 15$<br /><br />Now we have the equation of line u in slope-intercept form: $y = \frac{3}{2}x - 15$. The slope of line u is $\frac{3}{2}$.<br /><br />Since line v is perpendicular to line u, the slope of line v will be the negative reciprocal of the slope of line u. Therefore, the slope of line v is $-\frac{2}{3}$.<br /><br />Step 3: Use the point-slope form of a linear equation to find the equation of line v. The point-slope form 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.<br /><br />Given point: $(2, -1)$<br />Slope: $-\frac{2}{3}$<br /><br />Substitute these values into the point-slope form:<br />$y - (-1) = -\frac{2}{3}(x - 2)$<br /><br />Simplify:<br />$y + 1 = -\frac{2}{3}x + \frac{4}{3}$<br /><br />Step 4: Rearrange the equation into slope-intercept form:<br />$y = -\frac{2}{3}x + \frac{4}{3} - 1$<br /><br />Combine like terms:<br />$y = -\frac{2}{3}x + \frac{1}{3}$<br /><br />Therefore, the equation of line v in slope-intercept form is:<br />$y = -\frac{2}{3}x + \frac{1}{3}$