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Graph the line of the equation $2x-y=6$ using its slope and y -intercept.
Graph the line of the equation $3x-2y=8$ using its slope and y -intercept.
We have used a grid with $x$ and $y$ both going from about $\mathrm{-10}$ to 10 for all the equations we’ve graphed so far. Not all linear equations can be graphed on this small grid. Often, especially in applications with real-world data, we’ll need to extend the axes to bigger positive or smaller negative numbers.
Graph the line of the equation $y=0.2x+45$ using its slope and y -intercept.
We’ll use a grid with the axes going from about $\mathrm{-80}$ to 80.
$y=mx+b$ | |
The equation is in slope–intercept form. | $y=0.2x+45$ |
Identify the slope and y -intercept. | $m=0.2$ |
The y -intercept is (0, 45) | |
Plot the y -intercept. | See graph below. |
Count out the rise and run to mark the second point. The slope is $m=0.2$ ; in fraction form this means $m=\frac{2}{10}$ . Given the scale of our graph, it would be easier to use the equivalent fraction $m=\frac{10}{50}$ . | |
Draw the line. |
Graph the line of the equation $y=0.5x+25$ using its slope and y -intercept.
Graph the line of the equation $y=0.1x-30$ using its slope and y -intercept.
Now that we have graphed lines by using the slope and y -intercept, let’s summarize all the methods we have used to graph lines. See [link] .
Now that we have seen several methods we can use to graph lines, how do we know which method to use for a given equation?
While we could plot points, use the slope–intercept form, or find the intercepts for any equation, if we recognize the most convenient way to graph a certain type of equation, our work will be easier. Generally, plotting points is not the most efficient way to graph a line. We saw better methods in sections 4.3, 4.4, and earlier in this section. Let’s look for some patterns to help determine the most convenient method to graph a line.
Here are six equations we graphed in this chapter, and the method we used to graph each of them.
Equations #1 and #2 each have just one variable. Remember, in equations of this form the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this form have graphs that are vertical or horizontal lines.
In equations #3 and #4, both $x$ and $y$ are on the same side of the equation. These two equations are of the form $Ax+By=C$ . We substituted $y=0$ to find the x -intercept and $x=0$ to find the y -intercept, and then found a third point by choosing another value for $x$ or $y$ .
Equations #5 and #6 are written in slope–intercept form. After identifying the slope and y -intercept from the equation we used them to graph the line.
This leads to the following strategy.
Consider the form of the equation.
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