A line passes through the point $$ (-4,-9) $$ and has a slope of $$ \frac{5}{4} $$. Write an equation in slope-intercept form for this line.

Question

UpStudy AI · Accepted Answer

We start with the slope-intercept form of a line:

$$
y = mx + b
$$

Given that the slope is $$ m = \frac{5}{4} $$, the equation becomes:

$$
y = \frac{5}{4}x + b
$$

Since the line passes through the point $$ (-4,-9) $$, we substitute $$ x = -4 $$ and $$ y = -9 $$ into the equation:

$$
-9 = \frac{5}{4}(-4) + b
$$

Simplify the right-hand side:

$$
\frac{5}{4}(-4) = -5
$$

Thus, the equation becomes:

$$
-9 = -5 + b
$$

Solve for $$ b $$ by adding $$ 5 $$ to both sides:

$$
b = -9 + 5 = -4
$$

Now substitute $$ b = -4 $$ back into the equation:

$$
y = \frac{5}{4}x - 4
$$
The equation of the line in slope-intercept form is $$ y = \frac{5}{4}x - 4 $$.

A line passes through the point \( (-4,-9) \) and has a slope of \( \frac{5}{4} \). Write an equation in slope-intercept form for this line.