A line passes through the point $$ (-6,6) $$ and has a slope of $$ \frac{4}{3} $$. Write an equation in point-slope form for this line. $$ \square $$

Question

UpStudy AI · Accepted Answer

1. The point-slope form of a line is given by
   $$
   y - y_1 = m(x - x_1).
   $$

2. Here, the slope is $$ m = \frac{4}{3} $$ and the point is $$ (x_1, y_1) = (-6, 6) $$.

3. Substituting these values into the point-slope formula, we get
   $$
   y - 6 = \frac{4}{3}(x - (-6)).
   $$

4. Simplify the expression inside the parentheses:
   $$
   x - (-6) = x + 6.
   $$

5. Thus, the equation becomes
   $$
   y - 6 = \frac{4}{3}(x + 6).
   $$

$$\boxed{y - 6 = \frac{4}{3}(x + 6)}$$
The equation in point-slope form is $$ y - 6 = \frac{4}{3}(x + 6) $$.

A line passes through the point \( (-6,6) \) and has a slope of \( \frac{4}{3} \). Write an equation in point-slope form for this line. \( \square \)