To find the equation of the line in slope-intercept form (which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept), we need to determine the slope and the y-intercept.

Step 1: Identify two points on the line.

From the image, it appears that two points on the line are:

• $(-5, 3)$
• $(1, 0)$

Step 2: Calculate the slope.

The slope $m$ is calculated by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-5, 3)$ and $(1, 0)$: $m = \frac{0 - 3}{1 - (-5)} = \frac{-3}{1 + 5} = \frac{-3}{6} = -\frac{1}{2}$

Step 3: Determine the y-intercept.

The slope-intercept form is $y = mx + b$. We already know the slope $m = -\frac{1}{2}$.

Now, substitute one of the points (let's use $(1, 0)$) into the equation to solve for $b$: $0 = -\frac{1}{2}(1) + b$ $0 = -\frac{1}{2} + b$ $b = \frac{1}{2}$

Step 4: Write the equation.

Thus, the equation of the line in slope-intercept form is: $y = -\frac{1}{2}x + \frac{1}{2}$

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:

1. How do you find the slope if you are given only two points?
2. What are the different forms of the equation of a line?
3. How can you graph a line given its slope-intercept form equation?
4. What does the slope represent geometrically?
5. How can you convert the slope-intercept form to the standard form?

Tip: The y-intercept is the point where the line crosses the y-axis, and it occurs when $x = 0$.