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Let me analyze the content first.The image contains a math problem about finding the equation of a line passing through two points.

The question appears to be:

**(a) Use slope-intercept form to write the equation of the line that passes through the two given points:**
\[
(1, -6) \quad \text{and} \quad (5, 6)
\]

### Part 1 of 2:
- The first part asks for **the equation of the line in slope-intercept form (y = mx + b)**, where \(m\) is the slope and \(b\) is the y-intercept.

### Part 2 of 2:
- The second part asks for **the equation of the line in point-slope form**, where you use one of the points and the slope to write the equation.

Let's begin solving this:

### Step 1: Finding the slope (m)
The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the given points \((1, -6)\) and \((5, 6)\):
\[
m = \frac{6 - (-6)}{5 - 1} = \frac{6 + 6}{4} = \frac{12}{4} = 3
\]
So, the slope \(m = 3\).

### Step 2: Finding the y-intercept (b)
Using the slope-intercept form \(y = mx + b\), substitute one of the points, say \((1, -6)\), and the slope \(m = 3\):
\[
-6 = 3(1) + b \implies -6 = 3 + b \implies b = -6 - 3 = -9
\]

So, the equation in slope-intercept form is:
\[
y = 3x - 9
\]

### Step 3: Equation in point-slope form
The point-slope form of a line equation is:
\[
y - y_1 = m(x - x_1)
\]
Substitute the slope \(m = 3\) and one of the points, say \((1, -6)\):
\[
y - (-6) = 3(x - 1) \implies y + 6 = 3(x - 1)
\]
This is the equation in point-slope form.

### Final Answer:
- Slope-intercept form: \(y = 3x - 9\)
- Point-slope form: \(y + 6 = 3(x - 1)\)

Do you want further details or have any questions? Here are five related questions for you to consider:

1. How do you convert from point-slope form to slope-intercept form?
2. How can you check if a point lies on the line of the equation?
3. What happens to the equation if the two points have the same x-coordinates?
4. How would the slope change if the points were reversed?
5. Can you graph the equation \(y = 3x - 9\) and identify the intercepts?

**Tip:** Always double-check your calculations by plugging the points back into the final equation to ensure they satisfy it.

Use slope-intercept form to write the equation of the line that passes through the two points (1, -6) and (5, 6).

Find the equation of a line that passes through the points (1, -6) and (5, 6) in slope-intercept and point-slope form. Learn step-by-step how to calculate the slope and use key algebraic formulas. Suitable for Grades 8-10.

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