A line passes through the points (–
12,9) and (13,–
11). Write its equation in slope-intercept form.


To find the equation of the line passing through the points \((-12, 9)\) and \((13, -11)\), we need to follow these steps:

### 1. **Find the slope (m)**
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points \((-12, 9)\) and \((13, -11)\):
\[
m = \frac{-11 - 9}{13 - (-12)} = \frac{-11 - 9}{13 + 12} = \frac{-20}{25} = -\frac{4}{5}
\]

### 2. **Use the point-slope form of the equation**
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, say \((-12, 9)\), and the slope \(m = -\frac{4}{5}\). Substituting these into the equation:
\[
y - 9 = -\frac{4}{5}(x - (-12)) = -\frac{4}{5}(x + 12)
\]

### 3. **Simplify and solve for \(y\)**
Now distribute the slope:
\[
y - 9 = -\frac{4}{5}x - \frac{4}{5} \times 12
\]
\[
y - 9 = -\frac{4}{5}x - \frac{48}{5}
\]

Now, add 9 to both sides:
\[
y = -\frac{4}{5}x - \frac{48}{5} + 9
\]
Convert 9 to a fraction with the same denominator:
\[
y = -\frac{4}{5}x - \frac{48}{5} + \frac{45}{5}
\]
\[
y = -\frac{4}{5}x - \frac{3}{5}
\]

### Final equation in slope-intercept form:
\[
y = -\frac{4}{5}x - \frac{3}{5}
\]

Let me know if you'd like more details on any part of this!

### Related questions:
1. How do you convert between point-slope form and slope-intercept form?
2. What are the key characteristics of the slope-intercept form?
3. How do you find the slope of a line if the equation is already given in standard form?
4. How would the equation change if the points were flipped?
5. What is the significance of the y-intercept in a linear equation?

### Tip:  
Always double-check your slope calculations to ensure you’re working with the correct steepness for your line!

A line passes through the points (–12,9) and (13,–11). Write its equation in slope-intercept form.

Discover how to find the equation of a line passing through points (–12, 9) and (13, –11) using the slope-intercept form. This step-by-step guide covers key algebraic concepts and formulas, including the slope formula and point-slope form. Ideal for students in Grades 8-10.

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