To find the values of $m$ (the slope) and $b$ (the y-intercept) for the line, we can use the slope-intercept form of a linear equation, which is:

$y = mx + b$

From the graph:

1. Y-intercept ($b$): This is where the line crosses the y-axis. Looking at the graph, the red line crosses the y-axis at $y = 2$. Therefore, $b = 2$.

2. Slope ($m$): The slope is the "rise over run," or the change in $y$ divided by the change in $x$. Let's use two clear points on the line. We can see the line passes through:

   • $(-4, -2)$
   • $(0, 2)$

   The slope is calculated as:

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

Thus, the values are:

• $m = 1$
• $b = 2$

Would you like any further explanation or clarification on this?

Related questions:

1. What is the general form of a linear equation?
2. How do you calculate the slope if the points are not visible clearly on a graph?
3. Can you explain the meaning of a positive vs. negative slope?
4. How can you find the equation of a line if only given the slope and one point?
5. What happens to the graph if the slope or intercept changes?

Tip:

The y-intercept ($b$) is always the point where the line crosses the y-axis, and the slope ($m$) determines the steepness and direction of the line.