Let's solve the equations of the lines in slope-intercept form ($y = mx + b$) for each numbered graph (22–27).

Here’s the process:

1. Find the slope ($m$):

   • Use two points on the line and apply the formula: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{\Delta y}{\Delta x}.$

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

   • Identify where the line crosses the y-axis.

Solution:

22.

• Points: $(-2, 4)$ and $(2, 0)$. $m = \frac{0 - 4}{2 - (-2)} = \frac{-4}{4} = -1.$ Y-intercept ($b$) is at $(0, 2)$.

  Equation: $y = -x + 2$.

23.

• Points: $(-2, -2)$ and $(2, 2)$. $m = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1.$ Y-intercept ($b$) is at $(0, 0)$.

  Equation: $y = x$.

24.

• Points: $(-2, 2)$ and $(2, -2)$. $m = \frac{-2 - 2}{2 - (-2)} = \frac{-4}{4} = -1.$ Y-intercept ($b$) is at $(0, 0)$.

  Equation: $y = -x$.

25.

• Points: $(-2, 4)$ and $(2, -4)$. $m = \frac{-4 - 4}{2 - (-2)} = \frac{-8}{4} = -2.$ Y-intercept ($b$) is at $(0, 0)$.

  Equation: $y = -2x$.

26.

• Points: $(-2, -2)$ and $(2, 2)$. $m = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1.$ Y-intercept ($b$) is at $(0, 0)$.

  Equation: $y = x$.

27.

• Points: $(-2, -2)$ and $(2, 2)$. $m = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1.$ Y-intercept ($b$) is at $(0, 0)$.

  Equation: $y = x$.

Would you like a detailed step-by-step for any specific graph?

Related Questions:

1. What does the slope ($m$) tell you about the line's direction?
2. How does the y-intercept ($b$) affect the graph of the line?
3. How would the equation change if the slope were steeper?
4. What is the significance of a slope of zero or an undefined slope?
5. Can the slope-intercept form be converted into standard form? How?

Tip: Always double-check the points you choose on the graph for accuracy when finding the slope.