To solve the problem, we need to find the slope of the line for each student's graph and then sum the three slopes. Let's go through this step by step.
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Step 1: Recall the formula for slope
The slope \( m \) of a line is given by:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are any two points on the line.
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Step 2: Analyze Student A's graph
- The line passes through the points \((0, 3)\) and \((4, 1)\).
- Using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}
\]
- Therefore, the slope for Student A is:
\[
m_A = -\frac{1}{2}
\]
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Step 3: Analyze Student B's graph
- The line passes through the points \((0, 4)\) and \((2, -2)\).
- Using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 4}{2 - 0} = \frac{-6}{2} = -3
\]
- Therefore, the slope for Student B is:
\[
m_B = -3
\]
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Step 4: Analyze Student C's graph
- The line passes through the points \((0, -2)\) and \((4, 0)\).
- Using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}
\]
- Therefore, the slope for Student C is:
\[
m_C = \frac{1}{2}
\]
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Step 5: Sum the slopes
Now, we add the slopes from all three students:
\[
m_A + m_B + m_C = -\frac{1}{2} + (-3) + \frac{1}{2}
\]
Simplify the expression:
\[
-\frac{1}{2} + \frac{1}{2} = 0
\]
So:
\[
0 + (-3) = -3
\]
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Final Answer
The sum of the slopes is:
\[
\boxed{-3}
\]
Parent Tip: Review the logic above to help your child master the concept of find slope and y intercept worksheet.
