To solve the problem of finding the slope and y-intercept of the straight-line graphs shown in the image, we need to analyze each graph individually. Here's a step-by-step explanation for each graph:
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Graph 1:
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Equation Form: \( y = mx + b \)
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Slope (\( m \)): The slope is the change in \( y \) divided by the change in \( x \). From the graph, as \( x \) increases by 1, \( y \) increases by 2. Therefore, the slope \( m = 2 \).
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y-Intercept (\( b \)): The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at \( y = 1 \). Therefore, the y-intercept \( b = 1 \).
Answer:
- Slope: \( m = 2 \)
- y-Intercept: \( b = 1 \)
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Graph 2:
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Slope (\( m \)): As \( x \) increases by 1, \( y \) increases by 1. Therefore, the slope \( m = 1 \).
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y-Intercept (\( b \)): The line crosses the y-axis at \( y = 0 \). Therefore, the y-intercept \( b = 0 \).
Answer:
- Slope: \( m = 1 \)
- y-Intercept: \( b = 0 \)
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Graph 3:
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Slope (\( m \)): As \( x \) increases by 1, \( y \) decreases by 1. Therefore, the slope \( m = -1 \).
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y-Intercept (\( b \)): The line crosses the y-axis at \( y = 2 \). Therefore, the y-intercept \( b = 2 \).
Answer:
- Slope: \( m = -1 \)
- y-Intercept: \( b = 2 \)
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Graph 4:
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Slope (\( m \)): As \( x \) increases by 1, \( y \) decreases by 2. Therefore, the slope \( m = -2 \).
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y-Intercept (\( b \)): The line crosses the y-axis at \( y = 3 \). Therefore, the y-intercept \( b = 3 \).
Answer:
- Slope: \( m = -2 \)
- y-Intercept: \( b = 3 \)
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Graph 5:
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Slope (\( m \)): As \( x \) increases by 1, \( y \) increases by 3. Therefore, the slope \( m = 3 \).
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y-Intercept (\( b \)): The line crosses the y-axis at \( y = -2 \). Therefore, the y-intercept \( b = -2 \).
Answer:
- Slope: \( m = 3 \)
- y-Intercept: \( b = -2 \)
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Graph 6:
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Slope (\( m \)): As \( x \) increases by 1, \( y \) decreases by 1. Therefore, the slope \( m = -1 \).
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y-Intercept (\( b \)): The line crosses the y-axis at \( y = -1 \). Therefore, the y-intercept \( b = -1 \).
Answer:
- Slope: \( m = -1 \)
- y-Intercept: \( b = -1 \)
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Final Answers:
1. Slope: \( m = 2 \), y-Intercept: \( b = 1 \)
2. Slope: \( m = 1 \), y-Intercept: \( b = 0 \)
3. Slope: \( m = -1 \), y-Intercept: \( b = 2 \)
4. Slope: \( m = -2 \), y-Intercept: \( b = 3 \)
5. Slope: \( m = 3 \), y-Intercept: \( b = -2 \)
6. Slope: \( m = -1 \), y-Intercept: \( b = -1 \)
\[
\boxed{
\begin{array}{ll}
1. & m = 2, b = 1 \\
2. & m = 1, b = 0 \\
3. & m = -1, b = 2 \\
4. & m = -2, b = 3 \\
5. & m = 3, b = -2 \\
6. & m = -1, b = -1 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of finding slope and y intercept from an equation worksheet.
