From the provided image, I see there are four graphs labeled $A$, $B$, $C$, and $D$, and the goal is to match them to specific properties regarding slope or equation.

Step-by-step Analysis:

1. Determine Slopes and Intercepts for Each Graph:

• The slope of a line ($m$) is determined by the ratio of the vertical change ($\Delta y$) to the horizontal change ($\Delta x$).
• The y-intercept is where the line crosses the y-axis.

Graph $A$:

• Observing the line, it rises as we move to the right, indicating a positive slope.
• Calculate slope:
  • Rise: From $(0, 2)$ to $(2, 7)$: $\Delta y = 7 - 2 = 5$, $\Delta x = 2 - 0 = 2$.
  • Slope $m = \frac{5}{2}$.
• Y-intercept: $(0, 2)$.
• Equation: $y = \frac{5}{2}x + 2$.

Graph $B$:

• The line slopes downward, indicating a negative slope.
• Calculate slope:
  • Fall: From $(0, 0)$ to $(-1, 4)$: $\Delta y = 0 - 4 = -4$, $\Delta x = 0 - (-1) = 1$.
  • Slope $m = -4$.
• Y-intercept: $(0, 0)$.
• Equation: $y = -4x$.

Graph $C$:

• The line slopes downward, indicating a negative slope.
• Calculate slope:
  • Fall: From $(0, -4)$ to $(5, -8)$: $\Delta y = -8 - (-4) = -4$, $\Delta x = 5 - 0 = 5$.
  • Slope $m = \frac{-4}{5}$.
• Y-intercept: $(0, -4)$.
• Equation: $y = -\frac{4}{5}x - 4$.

Graph $D$:

• The line rises as we move to the right, indicating a positive slope.
• Calculate slope:
  • Rise: From $(0, 2)$ to $(2, 4)$: $\Delta y = 4 - 2 = 2$, $\Delta x = 2 - 0 = 2$.
  • Slope $m = 1$.
• Y-intercept: $(0, 2)$.
• Equation: $y = x + 2$.

Answers:

1. Which graph has a slope of $5/2$?
   Answer: $A$.

2. Which graph has a slope of $-4$?
   Answer: $B$.

3. Which graph has an equation of $y = x + 2$?
   Answer: $D$.

4. Which graph has an equation of $y = -\frac{4}{5}x - 4$?
   Answer: $C$.

Would you like further explanation or assistance? 😊

Related Questions:

1. How can you calculate the slope of a line using two points?
2. What is the significance of a negative slope in a graph?
3. How do you identify the y-intercept directly from a graph?
4. Can a line have a slope of 0? What does this look like on a graph?
5. What does it mean if a line has an undefined slope?

Tip: Always double-check your rise-over-run calculations to ensure slope accuracy!