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

To find the equation of a line in slope-intercept form, we use the formula:

$$
y = mx + b
$$

where $$ m $$ is the slope and $$ b $$ is the y-intercept.

Given:
- The slope $$ m = \frac{5}{4} $$
- A point on the line $$ (-4, -9) $$

We can substitute the slope and the coordinates of the point into the equation to find $$ b $$.

1. Substitute $$ x = -4 $$, $$ y = -9 $$, and $$ m = \frac{5}{4} $$ into the equation:

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

2. Calculate $$ \frac{5}{4}(-4) $$:

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

3. Substitute this value back into the equation:

$$
-9 = -5 + b
$$

4. Solve for $$ b $$:

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

Now we have both $$ m $$ and $$ b $$:
- Slope $$ m = \frac{5}{4} $$
- Y-intercept $$ b = -4 $$

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

$$
y = \frac{5}{4}x - 4
$$
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.