To graph the equation \( y = \frac{5}{6}x + 1 \), you'll need to plot points by substituting values for \( x \) and finding the corresponding \( y \) values.
Here's a step-by-step guide:
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Choose x-values from the range -10 to 10. Let's use a few values for simplicity: -10, -6, -2, 0, 2, 6, and 10.
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Calculate y-values using the equation:
- For \( x = -10 \): \[ y = \frac{5}{6}(-10) + 1 = -\frac{50}{6} + 1 = -\frac{50}{6} + \frac{6}{6} = -\frac{44}{6} \approx -7.33 \]
- For \( x = -6 \): \[ y = \frac{5}{6}(-6) + 1 = -5 + 1 = -4 \]
- For \( x = -2 \): \[ y = \frac{5}{6}(-2) + 1 = -\frac{10}{6} + 1 = -\frac{10}{6} + \frac{6}{6} = -\frac{4}{6} \approx -0.67 \]
- For \( x = 0 \): \[ y = \frac{5}{6}(0) + 1 = 1 \]
- For \( x = 2 \): \[ y = \frac{5}{6}(2) + 1 = \frac{10}{6} + 1 = \frac{10}{6} + \frac{6}{6} = \frac{16}{6} \approx 2.67 \]
- For \( x = 6 \): \[ y = \frac{5}{6}(6) + 1 = 5 + 1 = 6 \]
- For \( x = 10 \): \[ y = \frac{5}{6}(10) + 1 = \frac{50}{6} + 1 = \frac{50}{6} + \frac{6}{6} = \frac{56}{6} \approx 9.33 \]
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Plot the points on a graph:
- \((-10, -7.33)\)
- \((-6, -4)\)
- \((-2, -0.67)\)
- \((0, 1)\)
- \((2, 2.67)\)
- \((6, 6)\)
- \((10, 9.33)\)
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Draw the line through these points. Since it's a linear equation, you can connect the points with a straight line.
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Label the axes from -10 to 10 for both the x and y axes.
If you need a visual representation, you can plot the points on graph paper or use graphing software. The line should slope upwards, reflecting the positive slope of \( \frac{5}{6} \).