Solutions

First Image

Write the linear equations with the given slopes and $y$-intercepts.

The general form of a linear equation is:

$y = mx + b$

Where:

• $m$ is the slope.
• $b$ is the $y$-intercept.

5. Slope = 4, $y$-intercept = 1
Substitute into $y = mx + b$:

$y = 4x + 1$

6. Slope = -8, $y$-intercept = -3
Substitute into $y = mx + b$:

$y = -8x - 3$

Second Image

We match the graphs with their corresponding linear equations by analyzing slope and y-intercept.

1. Graph 1:

   • Positive slope (line increases).
   • $y$-intercept at $(0, 1)$.
   • Equation: $y = x + 1$ → Option A.

2. Graph 2:

   • Negative slope (line decreases).
   • $y$-intercept at $(0, 5)$.
   • Equation: $y = -\frac{7}{2}x - 1$ → Option F.

3. Graph 3:

   • Negative slope (line decreases).
   • $y$-intercept at $(0, 2)$.
   • Equation: $y = -\frac{3}{4}x + 2$ → Option G.

4. Graph 4:

   • Positive slope (line increases).
   • $y$-intercept at $(0, -5)$.
   • Equation: $y = 2x - 5$ → Option H.

Summary of Matches

1. Graph 1 → A $y = x + 1$
2. Graph 2 → F $y = -\frac{7}{2}x - 1$
3. Graph 3 → G $y = -\frac{3}{4}x + 2$
4. Graph 4 → H $y = 2x - 5$

Do you need further explanations for these matches or equations?

Related Questions:

1. How do you determine the slope from a graph?
2. How can you find the equation of a line given two points?
3. What happens to the graph of a line if the slope increases?
4. What is the effect of a positive versus negative slope on the graph?
5. How do you calculate the $y$-intercept if you know the slope and a point on the line?

Tip:

To determine the slope of a line on a graph, use the rise over run formula:
$m = \frac{\text{change in } y}{\text{change in } x}.$