To solve for the equation of the line in the graph:

Step 1: Identify two points on the line

From the graph:

• One point is $(-4, 2)$.
• Another point is $(2, -2)$.

Step 2: Calculate the slope ($m$) of the line

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points: $m = \frac{-2 - 2}{2 - (-4)} = \frac{-4}{6} = -\frac{2}{3}$

Step 3: Use the point-slope form of a line

The point-slope form is: $y - y_1 = m(x - x_1)$ Using the point $(-4, 2)$ and $m = -\frac{2}{3}$: $y - 2 = -\frac{2}{3}(x - (-4))$ $y - 2 = -\frac{2}{3}(x + 4)$

Step 4: Simplify to slope-intercept form ($y = mx + b$)

Expand: $y - 2 = -\frac{2}{3}x - \frac{8}{3}$ Add $2$ to both sides: $y = -\frac{2}{3}x - \frac{8}{3} + 2$ Express $2$ as $\frac{6}{3}$: $y = -\frac{2}{3}x - \frac{8}{3} + \frac{6}{3}$ Simplify: $y = -\frac{2}{3}x - \frac{2}{3}$

Final Answer:

$y = -\frac{2}{3}x - \frac{2}{3}$

Would you like more details or help with related questions?

Related Questions:

1. What does the slope represent in the context of a line?
2. How do you calculate the slope if the points are fractions or decimals?
3. Can you verify this result by substituting the points into the equation?
4. What is the significance of the y-intercept in the equation?
5. How can we graph a line given its equation?

Tip: Always simplify your slope and intercept terms fully to avoid calculation errors.