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To write the equation of the line in slope-intercept form that passes through the points \((5, -12)\) and \((-3, -4)\), we need to find the slope \(m\) and the y-intercept \(b\) of the line.

### Step 1: Find the Slope \(m\)
The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((5, -12)\) and \((-3, -4)\):
- \(x_1 = 5\), \(y_1 = -12\)
- \(x_2 = -3\), \(y_2 = -4\)

Plugging these values into the slope formula:
\[
m = \frac{-4 - (-12)}{-3 - 5} = \frac{-4 + 12}{-8} = \frac{8}{-8} = -1
\]

So, the slope \(m = -1\).

### Step 2: Use Point-Slope Form to Find the Equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]

We’ll use the point \((5, -12)\) and the slope \(m = -1\):
\[
y - (-12) = -1(x - 5)
\]

Simplify this equation:
\[
y + 12 = -x + 5
\]

Subtract 12 from both sides to solve for \(y\):
\[
y = -x - 7
\]

### Final Answer
The equation of the line in slope-intercept form \(y = mx + b\) is:
\[
y = -x - 7
\]

Would you like further explanation or have any questions?

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Here are some related questions you might find useful to try:

1. What is the general form of a linear equation, and how do you convert from slope-intercept form to general form?
2. How do you determine if two lines are parallel or perpendicular by comparing their slopes?
3. What is the point-slope form of a line, and when is it useful?
4. How can you find the x-intercept of the line given by \(y = -x - 7\)?
5. If you were given only one point and the slope, how would you find the line's equation?

**Tip:** Remember, in slope-intercept form \(y = mx + b\), \(m\) represents the slope, and \(b\) represents the y-intercept where the line crosses the y-axis.

Write the equation of the line in slope-intercept form that goes through the points (5, -12) and (-3, -4).

Learn how to find the equation of a line in slope-intercept form that passes through the points (5, -12) and (-3, -4). This step-by-step solution covers key concepts like slope calculation and linear equations. Ideal for students in Grades 8-10.

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