Let's analyze and solve the problems shown in the two uploaded images.

Image 1: Problems 13–16

13) How many solutions are there for the system:
$y = 0.75x - 2$
$y = -0.75x + 2$
Solution:

• The slopes ($m$) are $0.75$ and $-0.75$, meaning the lines intersect at one point.
• Answer: One solution.

14) How many solutions for the system:
$y = -6x + 8$
$8 - 6x = y$
Solution:

• Both equations simplify to the same line ($y = -6x + 8$).
• Answer: Infinitely many solutions.

15) How many solutions (based on the graph):

• The graph shows two lines intersecting at one point.
• Answer: One solution.

16) Find the slope (graph):

• Slope ($m$) = $\frac{\text{rise}}{\text{run}} = \frac{-6}{3} = -2$.
• Answer: Slope = $-2$.

Image 2: Problems 17–24

17) Write the equation ($y = mx + b$):

• From the graph, slope $m = \frac{4}{5}$ (rise/run).
• The y-intercept is $b = 0$.
• Answer: $y = \frac{4}{5}x$.

18) Find the slope (graph):

• Slope $m = \frac{\text{rise}}{\text{run}} = \frac{3}{2}$.
• Answer: Slope = $\frac{3}{2}$.

19) Calculate the slope for points $(5, 4)$ and $(-4, 3)$:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{-4 - 5} = \frac{-1}{-9} = \frac{1}{9}.$

• Answer: Slope = $\frac{1}{9}$.

20) Identify slope and y-intercept:
$y = -3x - 10$

• Slope $m = -3$.
• Y-intercept $b = -10$.
• Answer: $m = -3, b = -10$.

21) Linear or nonlinear?

• (a) $y = 3x^2$ → Nonlinear (squared term).
• (b) $y = 2x$ → Linear.
• (c) $y = \frac{5}{x}$ → Nonlinear (reciprocal).
• Answer: (a) Nonlinear, (b) Linear, (c) Nonlinear.

22) Graph the table:

• Points: $(4, 8), (3, 6), (2, 4), (5, 10)$.
• Connect for a straight line (linear relationship).
• Answer: Linear graph.

23) Is this a function?

• Each input ($x$) has a unique output ($y$), so yes, this is a function.
• Answer: Yes.

24) Is this a function?

• The graph fails the vertical line test, so no, this is not a function.
• Answer: No.

Do you want detailed explanations for any of these?

Related Questions:

1. How can you determine the number of solutions for systems of equations using slopes?
2. Why does the vertical line test work for identifying functions?
3. How do you identify if a graph represents a linear equation?
4. What is the significance of the slope in real-world applications?
5. How can graphing help verify solutions to equations?

Tip:

Always label your axes and scales clearly when graphing equations—it helps in accurately identifying solutions!