From the image, we are tasked with identifying the equation of the red line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the y-intercept ($b$)

The red line intersects the y-axis at $y = 2$. Thus, $b = 2$.

Step 2: Find the slope ($m$)

The slope $m$ is calculated as: $m = \frac{\text{rise}}{\text{run}}$ From the graph:

• Starting at the y-intercept $(0, 2)$, another point on the line is $(4, 4)$.
• Rise = $4 - 2 = 2$
• Run = $4 - 0 = 4$

Thus: $m = \frac{2}{4} = \frac{1}{2}$

Step 3: Write the equation

Substitute $m = \frac{1}{2}$ and $b = 2$ into $y = mx + b$: $y = \frac{1}{2}x + 2$

The correct equation of the line is: $y = \frac{1}{2}x + 2$

If you have further questions or want detailed explanations for any part, let me know!

Related Questions:

1. How can you verify the equation of a line from a graph?
2. What is the general form of a linear equation, and how is it different from slope-intercept form?
3. How do you calculate the slope between two points without a graph?
4. How can you use the point-slope form to write the equation of a line?
5. What is the importance of slope and y-intercept in real-life applications?

Tip:

Always double-check the y-intercept and slope using at least two distinct points on the graph!