How to Graph Linear Equations Using the Slope & the Y Intercept
The slope-intercept form of a linear equation, in contrast to the standard form, is a powerful tool for graphing and visualizing linear relationships. In the slope-intercept form, the relevant aspects of a line are immediately apparent, and the relationship between the two variables is easy to visualize. Graphing, then, becomes a task of either mapping out the line's slope and y-intercept or plotting individual points using the slope-intercept equation.
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Instructions
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Using the Slope-Intercept Equation
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1
Write the equation in slope-intercept form (y = mx + b). For example, if the equation is written 4x + 2y = 10, rewrite it by isolating and solving for y:
2y = -4x + 10
y = -2x + 5 -
2
Locate the y-intercept (the b value in y = mx + b). In the example given, the y-intercept is 5. In other words, when x = 0, y = 5. The line crosses the y-axis at y = 5. Mark that point on the y-axis of your graph.
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3
Locate the slope of your line (the m value in y = mx + b). This tells you how many spaces you move up for each space moved over. For example, if your line has a slope of 2, move up two units for each unit moved right. A negative slope indicates downward change as you move from left to right.
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4
Draw a line of the correct slope from your y-intercept. A straightedge will help you draw a neat line in this process.
Plotting Points
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5
Write the equation of the line in slope-intercept form.
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6
Locate the y-intercept value (b) and mark it on your graph paper.
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7
Plug an x value into the equation and solve for the corresponding y value. These form the coordinates of a point. Plot this point on your graph paper. Repeat this process for as many points as you wish (three is usually a good number of points, allowing you to draw a neat straight line). The line is defined by just the y-intercept and one other point, but calculating one or two additional points is a good way to check your work.
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8
Connect the points.
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