Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible. See Example 2.

passes through (−2, 2) and (2, −8)
 
 

Additional Materials

To find the equation of the line that passes through two points, we follow these steps:

1. **Find the slope** using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

2. **Use the point-slope form** of a line equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   and convert it to the slope-intercept form \(y = mx + b\).

### Step 1: Calculate the slope \(m\)

We have the points \((-2, 2)\) and \((2, -8)\).

\[
m = \frac{-8 - 2}{2 - (-2)} = \frac{-10}{4} = -\frac{5}{2}
\]

### Step 2: Use point-slope form

We can choose one of the points, say \((-2, 2)\), to substitute into the point-slope form.

\[
y - 2 = -\frac{5}{2}(x - (-2))
\]

Simplify the equation:

\[
y - 2 = -\frac{5}{2}(x + 2)
\]
\[
y - 2 = -\frac{5}{2}x - 5
\]
\[
y = -\frac{5}{2}x - 5 + 2
\]
\[
y = -\frac{5}{2}x - 3
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -\frac{5}{2}x - 3
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you derive the equation of a line from its slope and a point on the line?
2. What is the significance of the slope in the slope-intercept form?
3. How do you convert point-slope form to slope-intercept form?
4. What are the steps to graph a line given its equation in slope-intercept form?
5. How can you check if a point lies on a given line?

### Tip:
When calculating the slope, always be careful with the signs of the coordinates to avoid mistakes in the equation.

Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible. See Example 2. Passes through (−2, 2) and (2, −8).

Learn how to find the equation of a line passing through the points (−2, 2) and (2, −8) using the slope-intercept form. This step-by-step solution covers important algebraic concepts like slope calculation and converting point-slope form to slope-intercept form. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation