Writing Linear Equations Review Worksheet - Free Printable

Problem Overview:

The task involves analyzing six linear equations and determining their slope and y-intercept. The equations are already provided in slope-intercept form, \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

We will extract the slope and y-intercept for each equation directly from their given forms.

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Solution:

#### Equation 1:
\[ y = \frac{2}{3}x + 5 \]

- Slope (\( m \)): The coefficient of \( x \) is \( \frac{2}{3} \).
- Y-intercept (\( b \)): The constant term is \( 5 \).

Answer:
- Slope: \( \frac{2}{3} \)
- Y-intercept: \( 5 \)

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#### Equation 2:
\[ y = -\frac{4}{7}x + 1 \]

- Slope (\( m \)): The coefficient of \( x \) is \( -\frac{4}{7} \).
- Y-intercept (\( b \)): The constant term is \( 1 \).

Answer:
- Slope: \( -\frac{4}{7} \)
- Y-intercept: \( 1 \)

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#### Equation 3:
\[ y = 6x - 3 \]

- Slope (\( m \)): The coefficient of \( x \) is \( 6 \).
- Y-intercept (\( b \)): The constant term is \( -3 \).

Answer:
- Slope: \( 6 \)
- Y-intercept: \( -3 \)

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#### Equation 4:
\[ y = -x - 9 \]

- Slope (\( m \)): The coefficient of \( x \) is \( -1 \) (since \( -x \) means \( -1x \)).
- Y-intercept (\( b \)): The constant term is \( -9 \).

Answer:
- Slope: \( -1 \)
- Y-intercept: \( -9 \)

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#### Equation 5:
\[ y = 10 \]

- Slope (\( m \)): This is a horizontal line, so the slope is \( 0 \).
- Y-intercept (\( b \)): The line crosses the y-axis at \( y = 10 \), so the y-intercept is \( 10 \).

Answer:
- Slope: \( 0 \)
- Y-intercept: \( 10 \)

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#### Equation 6:
\[ y = \frac{7}{2}x \]

- Slope (\( m \)): The coefficient of \( x \) is \( \frac{7}{2} \).
- Y-intercept (\( b \)): There is no constant term, so the y-intercept is \( 0 \).

Answer:
- Slope: \( \frac{7}{2} \)
- Y-intercept: \( 0 \)

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Final Answers:

1. Equation 1:
- Slope: \( \frac{2}{3} \)
- Y-intercept: \( 5 \)

2. Equation 2:
- Slope: \( -\frac{4}{7} \)
- Y-intercept: \( 1 \)

3. Equation 3:
- Slope: \( 6 \)
- Y-intercept: \( -3 \)

4. Equation 4:
- Slope: \( -1 \)
- Y-intercept: \( -9 \)

5. Equation 5:
- Slope: \( 0 \)
- Y-intercept: \( 10 \)

6. Equation 6:
- Slope: \( \frac{7}{2} \)
- Y-intercept: \( 0 \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Equation 1:} & \text{Slope: } \frac{2}{3}, \text{ Y-intercept: } 5 \\
\text{Equation 2:} & \text{Slope: } -\frac{4}{7}, \text{ Y-intercept: } 1 \\
\text{Equation 3:} & \text{Slope: } 6, \text{ Y-intercept: } -3 \\
\text{Equation 4:} & \text{Slope: } -1, \text{ Y-intercept: } -9 \\
\text{Equation 5:} & \text{Slope: } 0, \text{ Y-intercept: } 10 \\
\text{Equation 6:} & \text{Slope: } \frac{7}{2}, \text{ Y-intercept: } 0 \\
\end{array}
}
\]