Write an equation for the line containing the points (2, −2) and (−2, 6). Find the x and
y-intercepts of the line, if any.

We will first find the equation of the line passing through the points \((2, -2)\) and \((-2, 6)\).

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

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

Substituting the coordinates \((2, -2)\) and \((-2, 6)\):

\[
m = \frac{6 - (-2)}{-2 - 2} = \frac{6 + 2}{-4} = \frac{8}{-4} = -2
\]

### Step 2: Use the point-slope form to find the equation of the line
The point-slope form of a line is:

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

Substituting \(m = -2\) and one of the points, say \((2, -2)\):

\[
y - (-2) = -2(x - 2)
\]

Simplifying:

\[
y + 2 = -2(x - 2)
\]
\[
y + 2 = -2x + 4
\]
\[
y = -2x + 2
\]

Thus, the equation of the line is:

\[
y = -2x + 2
\]

### Step 3: Find the x-intercept and y-intercept

1. **Y-intercept**: The y-intercept is where the line crosses the y-axis, which occurs when \(x = 0\). Substituting \(x = 0\) into the equation:

\[
y = -2(0) + 2 = 2
\]

Thus, the y-intercept is \((0, 2)\).

2. **X-intercept**: The x-intercept is where the line crosses the x-axis, which occurs when \(y = 0\). Setting \(y = 0\) in the equation:

\[
0 = -2x + 2
\]

Solving for \(x\):

\[
2x = 2 \quad \Rightarrow \quad x = 1
\]

Thus, the x-intercept is \((1, 0)\).

### Final Answer:
- The equation of the line is: \(y = -2x + 2\)
- The x-intercept is: \((1, 0)\)
- The y-intercept is: \((0, 2)\)

Would you like more details or have any questions?

Here are some related questions for you to explore:
1. How do you find the slope of a line if one point is at infinity?
2. What is the general form of a linear equation, and how does it relate to slope-intercept form?
3. How do you calculate the distance between two points on a line?
4. What is the significance of the intercepts in graphing linear equations?
5. Can a line have more than one x-intercept or y-intercept?

**Tip:** Always double-check your intercepts by substituting the values back into the original equation to verify they satisfy the equation!

Write an equation for the line containing the points (2, −2) and (−2, 6). Find the x and y-intercepts of the line, if any.

Learn how to find the equation of a line passing through points (2, -2) and (-2, 6) and determine the x and y intercepts. This algebra problem covers concepts such as slope, point-slope form, and slope-intercept form. Suitable for Grades 8-10.

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