Write an equation of the line that passes through the given points.
(-2,7) (3,-8)

To find the equation of the line that passes through the points \((-2, 7)\) and \((3, -8)\), we will use the **point-slope form** of a line and calculate the slope first.

### Step 1: Calculate the slope (\(m\))
The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the points \((-2, 7)\) as \((x_1, y_1)\) and \((3, -8)\) as \((x_2, y_2)\):
\[
m = \frac{-8 - 7}{3 - (-2)} = \frac{-8 - 7}{3 + 2} = \frac{-15}{5} = -3
\]

### Step 2: Use the point-slope form
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]

Using the slope \(m = -3\) and one of the points, say \((-2, 7)\):
\[
y - 7 = -3(x - (-2))
\]
Simplify:
\[
y - 7 = -3(x + 2)
\]
\[
y - 7 = -3x - 6
\]
\[
y = -3x + 1
\]

### Final Equation
The equation of the line in slope-intercept form is:
\[
y = -3x + 1
\]

Would you like me to explain further or verify with the second point?

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#### 5 Related Questions:
1. How do you find the equation of a line if the slope and one point are given?
2. Can you rewrite this equation in standard form \(Ax + By = C\)?
3. How do you determine if two lines are parallel or perpendicular?
4. How would you graph this line using its equation?
5. What happens if you only know the \(x\)- and \(y\)-intercepts of a line?

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**Tip:** Always simplify the slope fully before substituting into the point-slope form to avoid errors.

Write an equation of the line that passes through the given points. (-2,7) (3,-8)

Learn how to find the equation of a line passing through the points (-2, 7) and (3, -8). This step-by-step guide covers calculating the slope, using the point-slope form, and simplifying to slope-intercept form. Suitable for Grades 8-10.

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