A line passes through the point $$ (-8,6) $$ and has a slope of $$ -\frac{5}{2} $$. Write an equation in point-slope form for this line.

Question

UpStudy AI · Accepted Answer

To write the equation of a line in point-slope form, we use the formula:

$$
y - y_1 = m(x - x_1)
$$

where $$ (x_1, y_1) $$ is a point on the line and $$ m $$ is the slope.

Given the point $$ (-8, 6) $$ and the slope $$ m = -\frac{5}{2} $$, we can substitute these values into the formula:

$$
y - 6 = -\frac{5}{2}(x - (-8))
$$

This simplifies to:

$$
y - 6 = -\frac{5}{2}(x + 8)
$$

Thus, the equation of the line in point-slope form is:

$$
y - 6 = -\frac{5}{2}(x + 8)
$$
The equation of the line in point-slope form is $$ y - 6 = -\frac{5}{2}(x + 8) $$.

A line passes through the point \( (-8,6) \) and has a slope of \( -\frac{5}{2} \). Write an equation in point-slope form for this line.