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Chapter 12—Graphing 124 Graphing Linear Equations Defining a Line in Terms of Its Slope and YIntercept You can define a line in terms of its slope and yintercept Let m = 2 and b = 4
Step 1: Plot the yintercept point. Step 2: Draw a straight line through the yintercept point, making certain the line has the given slope.
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Examples & Exercises
The SlopeIntercept Equation for a Straight Line The slopeintercept equation is a linear equation that completely defines a straight line on the coordinate plane.
Given the slope and yintercept of a line, determine its xintercept. In the equation y = mx + b Given the values for m and b, you can also find the yintercept This is done by setting y = 0 and solving for x y = mx + b 0 = mx + b x = b/m
Examples & Exercises
Introduction to Linear Equations
Here are four examples of linear equations and interpretations of their components:
So you can directly determine the slope and yintercept of a straight line directly from its linear equations. But what about the xintercept? That takes just a bit more work. To determine the xintercept from a linear equation:
Consider the first equation in the examples above: y = 2x + 4
How about the second equation: y = x  8
So the xoffset is (8,0) The equation y = 2 has no xintercept because the line is parallel to the xaxis To determine the xintercept for equation y = x:
Examples & Exercises
slopeintercept form.
More Examples 1. Plot the linear equation y = 2x + 1 The simplest approach is to determine the two intercepts, and this means solving the equations twice: first with x = 0 and then again with y = 0 y = 2x + 1 Substituting 0 for x y = 2 x 0 + 1 y = 1 One possible point on the line is its llllll (0,1) Solve again, but with y set to 0: y = 2x + 1 0 = 2x + 1 2x = 1 x = 0.5 (0.5,0) So the intercepts are two possible points on the line
Exercises


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