The first image shows a graph of a line with three given points: $(-8, -8)$, $(0, 6)$, and $(8, 4)$.

To determine the correct equation of the line in slope-intercept form, we need to find the slope and the y-intercept.

Step 1: Find the slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 6)$ and $(8, 4)$, we can calculate the slope: $m = \frac{4 - 6}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}$

Step 2: Find the y-intercept ($b$)

The general slope-intercept form of a line is: $y = mx + b$ We already know the slope $m = -\frac{1}{4}$, and we can use the point $(0, 6)$ (where $x = 0$) to find $b$. Substituting into the equation: $6 = -\frac{1}{4}(0) + b$ $b = 6$

Step 3: Write the equation

The equation of the line in slope-intercept form is: $y = -\frac{1}{4}x + 6$

Correct answer:

The correct equation is:
$y = -\frac{1}{4}x + 6$

This matches the second option in the second image.

Would you like further clarification or any other help? Here are some related questions you might find interesting:

1. How do you find the slope between two points when they are given in a graph?
2. What are other forms of linear equations, such as point-slope form and standard form?
3. How can you find the equation of a line when you are given only one point and the slope?
4. What is the significance of the y-intercept in a linear equation?
5. How do you graph a line from its slope-intercept form?

Tip: When solving for the slope, always double-check your calculation to avoid small errors!