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Then we can calculate the slope by finding the rise and run. We can choose any two points, but let’s look at the point $(-2,0).$ To get from this point to the y- intercept, we must move up 4 units (rise) and to the right 2 units (run). So the slope must be
Substituting the slope and y- intercept into the slope-intercept form of a line gives
Given a graph of linear function, find the equation to describe the function.
Match each equation of the linear functions with one of the lines in [link] .
Analyze the information for each function.
Now we can re-label the lines as in [link] .
So far, we have been finding the y- intercepts of a function: the point at which the graph of the function crosses the y -axis. A function may also have an x -intercept, which is the x -coordinate of the point where the graph of the function crosses the x -axis. In other words, it is the input value when the output value is zero.
To find the x -intercept, set a function $f(x)$ equal to zero and solve for the value of $x.$ For example, consider the function shown.
Set the function equal to 0 and solve for $x.$
The graph of the function crosses the x -axis at the point $\left(2,\text{0}\right).$
Do all linear functions have x -intercepts?
No. However, linear functions of the form $y=c,$ where $c$ is a nonzero real number are the only examples of linear functions with no x-intercept. For example, $y=5$ is a horizontal line 5 units above the x-axis. This function has no x-intercepts, as shown in [link] .
The x -intercept of the function is value of $x$ when $f(x)=0.$ It can be solved by the equation $0=mx+b.$
Find the x -intercept of $f(x)=\frac{1}{2}x-3.$
Set the function equal to zero to solve for $x.$
The graph crosses the x -axis at the point $\left(6,\text{0}\right).$
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