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You know that the slope of a line measures how steep the line is. In this lesson you will learn how to find an equation for a line if you know its slope and a point on the line, or two points on the line.
To the left is the graph of $y=2x+1$. Remember that this equation is in slope-intercept form, so 2 is the slope of the line and 1 indicates where the line crosses the $y$-axis. Use the sliders to change the values of $m$ and $b$ and notice how they affect the graph. Complete this table by using the sliders.
Complete this table. Use the sliders to check your answers.
In the last section you found an equation for a line given its slope and a particular point on the line, its $y$-intercept. In this section you will learn how to find an equation for a line given its slope and any point on the line, not necessarily the $y$-intercept.
Use the sliders to change the values of $m$, $x_1$, and $y_1$ and notice how they affect the graph of $y-y_1=m(x-x_1)$ and the plotted point $(x_1,y_1)$. The equation for the line is always shown below the grid. Use the sliders to complete this table.
If a line contains the point $(x_1,y_1)$ and has slope $m$, then its equation can be written as $y-y_1=m(x-x_1)$. $y-y_1=m(x-x_1)$ is called the point-slope form of the equation for a line.
You can write the equation $y-4=2(x-3)$ in slope-intercept form:
The first two equations you found in sameLineEqs are given again in the table below. Write them in slope-intercept form.
Sometimes we don’t know the slope of a line, but we do know two points on the line. For example, you might be told that the price of 4 baskets of strawberries is \$6 and the price of 2 baskets of strawberries is \$3. This means that you have two points, $(4,6)$ and $(2,3)$. To find an equation for the line through these points you need to find the slope first.
Write the equation you found in slope-intercept form.
By performing the following steps, write an equation for the line that passes through $(3,1)$ and $(4,-1)$ in slope-intercept form.
Finally, rewrite the equation in slope-intercept form.