To find the equation of the given line in slope-intercept form $y = mx + b$, let's identify the slope $m$ and the y-intercept $b$ from the graph.

1. Determine the Slope ($m$):

The slope can be calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's choose two points from the graph:

• Point 1: $(-2, 4)$
• Point 2: $(4, -2)$

Now calculate the slope: $m = \frac{-2 - 4}{4 - (-2)} = \frac{-6}{6} = -1$

2. Find the Y-intercept ($b$):

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, 2)$. Thus, $b = 2$.

3. Write the Equation:

Using $m = -1$ and $b = 2$, the equation of the line is: $y = -x + 2$

Would you like a detailed explanation on any specific part?

Related Questions:

1. How do you find the slope when only given two points?
2. What are the characteristics of a line when the slope is negative?
3. How do you determine the y-intercept if it isn’t clearly visible on a graph?
4. What does the slope-intercept form $y = mx + b$ represent geometrically?
5. How would the graph change if the slope was positive instead of negative?

Tip:

When finding the slope, always remember to subtract $y$-coordinates and $x$-coordinates in the same order to avoid sign errors.