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The slope of a line is a number that measures how steep the line is. In this lesson
you will learn about the meaning of slope, and find the slopes of several linear graphs.
Click to graph the equation $y=2x$ on the
grid to the left.
Use the slider in the lower left portion of your screen to change the value of
$m$ and answer the following questions.
When you slide $m$ the graph of $y=mx$
changes in steepness. The measure of this steepness is called the slope of the line.
The slope of a line is the amount of change in
the height of the line each time you go 1 unit to the right.
The equations $y_1=-x$ and
$y_2=-2x$ are graphed on the grid to the left.
The line shown below has slope $-1$ because as the $x$-coordinate is increased
by 1 you must move down 1 (in the $-1$ direction) to return to the line.
Use the slider and the graph to the left to complete the table below.
Use the grid to determine the slope of the green line.
You don’t need to see the graph of an equation to find its slope. Instead, you can
just use the equation to determine how much $y$ changes when you increase $x$ by 1.
In each row of the table, find the slope of $y=2x$ by
subtracting its $y$-values at the two indicated points, where $x$ increases by 1. The line, and
your two points, will be plotted on the grid to the left.
Notice that you can calculate the slope starting anywhere on the line, and you’ll get the
Because you get the same slope for a straight line wherever you start from, you might as well
pick simple $x$-values to use. The simplest $x$-values are almost always $x=0$ and $x=1$.
Find the slopes of these lines by subtracting their $y$-values when $x=0$ and
As you can see from the last few questions:
The slope of the line $y=mx$ is $m$.