Question

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$ (-9,-6), m=-\frac{2}{3} $$

Short answer

The point-slope form is: y + 6 = -2/3 * (x + 9). The slope-intercept form is: y = -2/3x -6.

Step-by-step solution

Insert values into the point-slope form

In the point-slope form, y - y1 = m(x - x1), replace m with -2/3, x1 with -9 and y1 with -6. That gives you the equation y - (-6) = -2/3 * (x- (-9)).

Simplify the equation

Simplify the equation and you get y + 6 = -2/3 * (x + 9).

Transform to the slope-intercept form

Transform the equation into the slope-intercept form y = mx + b, by isolating y. This gives you the equation y = -2/3x -6.