Question

Write the equation of a line that is perpendicular to the given line that passes through the given point.

Answer 1

Answer:

First we must find the opposite-reciprocal of the original slope.

current slope: $\frac{7}{3}$

new slope: $-\frac{3}{7}$

Using the new slope and the given point, we will plug them into slope-intercept form and solve for b, the y-intercept.

$9 = -\frac{3}{7}(-4) + b\\\\9 = \frac{12}{7} + b\\\\-\frac{51}{7} = b$

The y-intercept is $-\frac{51}{7}$.

Now, we can write the formula for the new line.

Slope-intercept form: $y = -\frac{3}{7}x - \frac{51}{7}$

Point-slope form: $y - 9 = -\frac{3}{7}(x + 4)$