It looks like you have uploaded an image containing a mathematical question. I will extract and interpret the text from the image to help solve it.

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.