https://file.aiquickdraw.com/mathbot/file/1729802461171brh506sq.jpg

Let's go through the problems one by one and find the equations in slope-intercept form \( y = mx + b \):

### 6) Points: \( (6, 11) \) and \( (9, 26) \)
First, find the slope \( m \) using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{26 - 11}{9 - 6} = \frac{15}{3} = 5
\]
Now, use the point-slope form \( y - y_1 = m(x - x_1) \) with point \( (6, 11) \):
\[
y - 11 = 5(x - 6)
\]
Simplifying:
\[
y - 11 = 5x - 30 \quad \Rightarrow \quad y = 5x - 19
\]
**Equation for 6**: \( y = 5x - 19 \)

---

### 7) Points: \( (14, -5) \) and \( (-10, 7) \)
Find the slope \( m \):
\[
m = \frac{7 - (-5)}{-10 - 14} = \frac{7 + 5}{-10 - 14} = \frac{12}{-24} = -\frac{1}{2}
\]
Using point \( (14, -5) \) in point-slope form:
\[
y - (-5) = -\frac{1}{2}(x - 14)
\]
Simplifying:
\[
y + 5 = -\frac{1}{2}x + 7 \quad \Rightarrow \quad y = -\frac{1}{2}x + 2
\]
**Equation for 7**: \( y = -\frac{1}{2}x + 2 \)

---

### 8) Table of values:
We can choose any two points from the table, for example \( (3, -20) \) and \( (6, 14) \). The slope is:
\[
m = \frac{14 - (-20)}{6 - 3} = \frac{14 + 20}{3} = \frac{34}{3}
\]
Using point \( (3, -20) \) in point-slope form:
\[
y - (-20) = \frac{34}{3}(x - 3)
\]
Simplifying:
\[
y + 20 = \frac{34}{3}x - 34 \quad \Rightarrow \quad y = \frac{34}{3}x - 54
\]
**Equation for 8**: \( y = \frac{34}{3}x - 54 \)

---

### 9) Graph:
From the graph, the line passes through \( (-4, -4) \) and \( (0, 2) \). Using the slope formula:
\[
m = \frac{2 - (-4)}{0 - (-4)} = \frac{2 + 4}{4} = \frac{6}{4} = \frac{3}{2}
\]
Using the point \( (0, 2) \), which is the y-intercept, the equation is:
\[
y = \frac{3}{2}x + 2
\]
**Equation for 9**: \( y = \frac{3}{2}x + 2 \)

---

Would you like more details on any of these steps, or do you have questions about the solutions?

### Related Questions:
1. How do you calculate the slope between two points?
2. What is the point-slope form of a line?
3. How can you find the equation of a line from a table of values?
4. What are the key steps to converting point-slope form to slope-intercept form?
5. How do you determine the slope and y-intercept from a graph?

### Tip:
Remember, the y-intercept is the value of \( y \) when \( x = 0 \). This can often simplify finding the equation of a line.

Write the equation in slope-intercept form for points, table, and graph provided in the image.

Learn how to write equations in slope-intercept form using points, tables, and graphs. This math problem involves calculating the slope and converting point-slope form to y = mx + b. Suitable for Grades 7-10.

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