Free Printable Writing Linear Equations Worksheet Collection - Free Printable

To solve the problem, we need to determine the slope and y-intercept for each graph and then write the equation of the line in slope-intercept form ($ y = mx + b $), where:
- $ m $ is the slope,
- $ b $ is the y-intercept.

Step-by-Step Solution:

#### Graph 1:
- Slope ($ m $): The line goes down as it moves to the right. To find the slope, choose two points on the line. For example, let's use the points $ (0, 3) $ and $ (4, -1) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{4 - 0} = \frac{-4}{4} = -1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 3) $. So, $ b = 3 $.
- Equation: Substitute $ m = -1 $ and $ b = 3 $ into $ y = mx + b $:
\[
y = -x + 3
\]

#### Graph 2:
- Slope ($ m $): The line goes up as it moves to the right. Choose two points on the line, such as $ (-2, -2) $ and $ (2, 2) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 0) $. So, $ b = 0 $.
- Equation: Substitute $ m = 1 $ and $ b = 0 $ into $ y = mx + b $:
\[
y = x
\]

#### Graph 3:
- Slope ($ m $): The line goes down as it moves to the right. Choose two points on the line, such as $ (0, 2) $ and $ (4, -2) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 2}{4 - 0} = \frac{-4}{4} = -1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 2) $. So, $ b = 2 $.
- Equation: Substitute $ m = -1 $ and $ b = 2 $ into $ y = mx + b $:
\[
y = -x + 2
\]

#### Graph 4:
- Slope ($ m $): The line goes up as it moves to the right. Choose two points on the line, such as $ (-2, -2) $ and $ (2, 2) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 0) $. So, $ b = 0 $.
- Equation: Substitute $ m = 1 $ and $ b = 0 $ into $ y = mx + b $:
\[
y = x
\]

#### Graph 5:
- Slope ($ m $): The line goes down as it moves to the right. Choose two points on the line, such as $ (0, 3) $ and $ (3, 0) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 3) $. So, $ b = 3 $.
- Equation: Substitute $ m = -1 $ and $ b = 3 $ into $ y = mx + b $:
\[
y = -x + 3
\]

#### Graph 6:
- Slope ($ m $): The line goes up as it moves to the right. Choose two points on the line, such as $ (-2, -2) $ and $ (2, 2) $.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1
\]
- y-intercept ($ b $): The line crosses the y-axis at $ (0, 0) $. So, $ b = 0 $.
- Equation: Substitute $ m = 1 $ and $ b = 0 $ into $ y = mx + b $:
\[
y = x
\]

Final Answers:

1. Graph 1:
- Slope = $ -1 $
- y-intercept = $ 3 $
- Equation: $ y = -x + 3 $

2. Graph 2:
- Slope = $ 1 $
- y-intercept = $ 0 $
- Equation: $ y = x $

3. Graph 3:
- Slope = $ -1 $
- y-intercept = $ 2 $
- Equation: $ y = -x + 2 $

4. Graph 4:
- Slope = $ 1 $
- y-intercept = $ 0 $
- Equation: $ y = x $

5. Graph 5:
- Slope = $ -1 $
- y-intercept = $ 3 $
- Equation: $ y = -x + 3 $

6. Graph 6:
- Slope = $ 1 $
- y-intercept = $ 0 $
- Equation: $ y = x $

Boxed Final Answer:

\[
\boxed{
\begin{array}{ccc}
\text{Graph 1:} & \text{Slope} = -1, & \text{y-intercept} = 3, & \text{Equation: } y = -x + 3 \\
\text{Graph 2:} & \text{Slope} = 1, & \text{y-intercept} = 0, & \text{Equation: } y = x \\
\text{Graph 3:} & \text{Slope} = -1, & \text{y-intercept} = 2, & \text{Equation: } y = -x + 2 \\
\text{Graph 4:} & \text{Slope} = 1, & \text{y-intercept} = 0, & \text{Equation: } y = x \\
\text{Graph 5:} & \text{Slope} = -1, & \text{y-intercept} = 3, & \text{Equation: } y = -x + 3 \\
\text{Graph 6:} & \text{Slope} = 1, & \text{y-intercept} = 0, & \text{Equation: } y = x \\
\end{array}
}
\]