Let's go through each graph to determine the equation of the line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Problem 24:

• The line crosses the y-axis at $y = 2$, so the y-intercept $b = 2$.
• To find the slope $m$, observe the change in $y$ and $x$ between two points on the line. For this line:
  • It goes down by 2 units in $y$ when moving 2 units to the right in $x$, giving a slope $m = \frac{-2}{2} = -1$.
• Equation: $y = -x + 2$.

Problem 25:

• The line crosses the y-axis at $y = 0$, so the y-intercept $b = 0$.
• For the slope $m$:
  • The line rises by 4 units in $y$ for a run of 2 units in $x$, giving a slope $m = \frac{4}{2} = 2$.
• Equation: $y = 2x$.

Problem 26:

• The line crosses the y-axis at $y = 2$, so the y-intercept $b = 2$.
• For the slope $m$:
  • The line goes down by 2 units in $y$ for a run of 2 units to the right in $x$, giving a slope $m = \frac{-2}{2} = -1$.
• Equation: $y = -x + 2$.

Problem 27:

• The line crosses the y-axis at $y = -2$, so the y-intercept $b = -2$.
• For the slope $m$:
  • The line rises by 2 units in $y$ for a run of 2 units in $x$, giving a slope $m = \frac{2}{2} = 1$.
• Equation: $y = x - 2$.

Summary of Equations:

1. 24: $y = -x + 2$
2. 25: $y = 2x$
3. 26: $y = -x + 2$
4. 27: $y = x - 2$

Would you like further explanations on any of these steps?

Relative Questions:

1. How is the slope calculated from a graph?
2. What does the y-intercept represent in the slope-intercept form of a line?
3. How can you determine if a line is increasing or decreasing from its equation?
4. Why does the slope change the direction of a line on a graph?
5. What happens to the graph if we change the slope or y-intercept in the equation?

Tip: Always look for two clear points on the line to determine the slope accurately.