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?

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.