Question

use the given conditions to write an equation for the line in point - slope form and slope - intercept form. slope = - 9, passing through (- 8, - 1). type the point - slope form of the line. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope, and $(x_1, y_1)$ is a point on the line.

Step2: Substitute given values

Here, $m = -9$, $x_1 = -8$, $y_1 = -1$. Substitute into the formula:
$y - (-1) = -9(x - (-8))$

Step3: Simplify the equation

Simplify the double negatives:
$y + 1 = -9(x + 8)$

Step4: Convert to slope-intercept form

First expand the right-hand side:
$y + 1 = -9x - 72$
Then subtract 1 from both sides to isolate $y$:
$y = -9x - 72 - 1$
$y = -9x - 73$

Answer:

Point-slope form: $y + 1 = -9(x + 8)$
Slope-intercept form: $y = -9x - 73$