A line passes through the point $$ (-4,-7) $$ 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**, which is:

$$
y = mx + b
$$

where:
- $$ m $$ is the slope of the line
- $$ b $$ is the y-intercept (the point where the line crosses the y-axis)

**Given:**
- Slope ($$ m $$) = $$ -\frac{5}{4} $$
- A point on the line = $$ (-4, -7) $$

**Steps to Find the Equation:**

1. **Plug the known values into the slope-intercept form.**

We know $$ m = -\frac{5}{4} $$ and the line passes through $$ (-4, -7) $$, so:

$$
   -7 = \left(-\frac{5}{4}\right)(-4) + b
   $$

2. **Solve for $$ b $$ (the y-intercept).**

$$
   -7 = \left(-\frac{5}{4}\right) \times (-4) + b
   $$
   
   $$
   -7 = 5 + b
   $$
   
   $$
   b = -7 - 5
   $$
   
   $$
   b = -12
   $$

3. **Write the final equation with the slope and y-intercept.**

$$
   y = -\frac{5}{4}x - 12
   $$

**Final Answer:**

$$
\boxed{y = -\dfrac{5}{4}\,x\ -\ 12}
$$
The equation of the line in slope-intercept form is $$ y = -\frac{5}{4}x - 12 $$.

A line passes through the point \( (-4,-7) \) and has a slope of \( -\frac{5}{4} \). Write an equation in slope-intercept form for this line.