Use the given conditions to write an equation for the line in​ point-slope form and​ slope-intercept form.
Passing through ​(negative 4​,13​) and ​(1​,negative 2​)

We are given two points, \((-4, 13)\) and \((1, -2)\). To find the equations of the line in point-slope form and slope-intercept form, we follow these steps:

### Step 1: Find the slope \( m \)
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points \((-4, 13)\) and \((1, -2)\):

\[
m = \frac{-2 - 13}{1 - (-4)} = \frac{-2 - 13}{1 + 4} = \frac{-15}{5} = -3
\]

### Step 2: Write the equation in point-slope form
The point-slope form of a line is:

\[
y - y_1 = m(x - x_1)
\]

Using the slope \( m = -3 \) and the point \((-4, 13)\):

\[
y - 13 = -3(x - (-4)) = -3(x + 4)
\]

Thus, the point-slope form is:

\[
y - 13 = -3(x + 4)
\]

### Step 3: Convert to slope-intercept form
To write the equation in slope-intercept form, we simplify the point-slope equation:

\[
y - 13 = -3(x + 4)
\]

Expand the right side:

\[
y - 13 = -3x - 12
\]

Add 13 to both sides:

\[
y = -3x - 12 + 13
\]

Simplify:

\[
y = -3x + 1
\]

### Final Answer:
- **Point-slope form**: \( y - 13 = -3(x + 4) \)
- **Slope-intercept form**: \( y = -3x + 1 \)

Do you want more details or have any questions?

Here are 5 relative questions for further exploration:
1. How would you find the equation if only one point and the slope were given?
2. What happens to the slope of a line when two points are switched?
3. How do you convert from slope-intercept form to point-slope form?
4. What does the slope of a line represent in real-life contexts?
5. How would you graph a line using its point-slope form?

**Tip:** Always double-check your slope calculation to avoid errors when solving for the equation of a line!

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through (-4, 13) and (1, -2).

Learn how to write the equation of a line passing through the points (-4, 13) and (1, -2) in both point-slope form and slope-intercept form. This problem covers key algebraic concepts such as the slope formula and linear equations, suitable for students in Grades 8-10.

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