2.1 Linear functions  (Page 5/17)

Therefore, the same line can be described in slope-intercept form as $y=-\frac{1}{2}x+7.$

Writing the equation of a line using a point and the slope

The point-slope form is particularly useful if we know one point and the slope of a line. Suppose, for example, we are told that a line has a slope of 2 and passes through the point $\left(4,1\right).$ We know that $m=2$ and that $x_1=4$ and $y_1=1.$ We can substitute these values into the general point-slope equation.

If we wanted to then rewrite the equation in slope-intercept form, we apply algebraic techniques.

Both equations, $y-1=2\left(x-4\right)$ and $y=2x–7,$ describe the same line. See [link] .

Writing the equation of a line using two points

The point-slope form of an equation is also useful if we know any two points through which a line passes. Suppose, for example, we know that a line passes through the points $\left(0,1\right)$ and $\left(3,2\right).$ We can use the coordinates of the two points to find the slope.

Now we can use the slope we found and the coordinates of one of the points to find the equation for the line. Let use (0, 1) for our point.

As before, we can use algebra to rewrite the equation in the slope-intercept form.

Both equations describe the line shown in [link] .