B. Graphing Linear Relations using an Equation in General Form
B. Graphing Linear Relations using an Equation in General Form
Linear relations whose equations are written in slope-intercept form can be graphed fairly quickly because the slope and
y-intercept of the graph are easily identified from the equation. The general form of a linear equation cannot be interpreted as readily. To graph a linear relation given in general form, the
x-intercept and the
y-intercept can be used.
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x-intercept
the point at which the graph of a relation crosses the x-axis |
In the
Investigation at the beginning of the lesson, you saw that the
x-intercept always occurs when
y = 0, and the
y-intercept always occurs when
x = 0. This means you can determine the
x-intercept by substituting 0 for
y into the general form equation and solving for
x. Similarly, you can determine the
y-intercept by substituting 0 for
x and solving for
y.
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Example 1 |
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Determine the x- and y-intercepts of the graph of the linear relation «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»5«/mn»«mi»y«/mi»«mo»+«/mo»«mn»15«/mn»«mo»=«/mo»«mn»0«/mn»«/math». The x-intercept occurs when y = 0, so substitute 0 for y and solve for x.
The x-intercept occurs at (−5,0). The y-intercept occurs when x = 0, so substitute 0 for x and solve for y.
The y-intercept occurs at (0,3) . |
A linear relation in general form can be graphed by plotting the
x- and
y-intercepts and then drawing a line through them.