Although I can't create visual graphs directly, I can guide you through how to plot the points and line with the specified slope.
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Identify the Point: You are starting with the point \((-1, -2)\).
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Determine the Slope: The slope is \(\frac{1}{3}\), which means for every 1 unit you move up (in the y-direction), you will move 3 units to the right (in the x-direction).
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Plot the Given Point: On a Cartesian plane, locate the point \((-1, -2)\) which is 1 unit left and 2 units down from the origin.
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Using the Slope to Find Another Point:
- From \((-1, -2)\), move up 1 unit (to \((-1, -1)\)) and then move 3 units to the right to \((2, -1)\).
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Plot the New Point: Plot the point \((2, -1)\).
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Draw the Line: Draw a straight line through the points \((-1, -2)\) and \((2, -1)\). This line will have a slope of \(\frac{1}{3}\).
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Equation of the Line: You can also find the equation of the line using the point-slope form: \[ y - y_1 = m(x - x_1) \] Plugging \((-1, -2)\) for \((x_1, y_1)\) and \(\frac{1}{3}\) for \(m\): \[ y + 2 = \frac{1}{3}(x + 1) \] Simplifying this gives: \[ y = \frac{1}{3}x - \frac{5}{3} \]
If you have graphing software or a graphing calculator, you can input the point and the slope to visualize it easily!
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