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.