The image shows a graph of a straight line. We are tasked with finding the equation of the line in slope-intercept form, which follows the formula:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept (the point where the line crosses the y-axis).

Steps to solve:

1. Identify the slope:

   • To find the slope, we need two points on the line.
   • Looking at the grid, it appears the line passes through $(0, 2)$ (the y-intercept) and $(-4, 0)$ (another clear point where the line crosses the x-axis).
   • The slope $m$ is calculated as the change in $y$ divided by the change in $x$:

   $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{-4 - 0} = \frac{-2}{-4} = \frac{1}{2}$

   So, the slope $m = \frac{1}{2}$.

2. Identify the y-intercept:

   • From the graph, the line crosses the y-axis at $(0, 2)$. Therefore, $b = 2$.

Final Equation:

Thus, the equation of the line in slope-intercept form is:

$y = \frac{1}{2}x + 2$

Would you like further clarification or more details on this process?

Relative Questions:

1. How do you determine the slope of a line using two points?
2. What is the slope-intercept form of a linear equation?
3. How does the y-intercept affect the position of a line?
4. Can a line have a negative slope? What would that look like?
5. How can you rewrite this equation in standard form?

Tip: Always pick two points that are easy to read on the graph to accurately calculate the slope.