What do you need to write a line equation in the point-slope form ?
Example Solution: y = - AB ( x - CA)
Practice makes perfect
We start with a line equation written in standard form, as shown below.
Ax + By = C
In our case we know that A and B are nonzero. To find the corresponding point-slope form, we need to find the slope m and a point (x_1,y_1). The point-slope form is shown below.
y - y_1 = m(x-x_1)The first thing to do is to find the slope. This can be done using the Slope Formula.
m = y_2-y_1/x_2-x_1
For this we require two known points, (x_1,y_1) and (x_2,y_2). A convenient choice for these are the x- and y-intercepts.
Finding the x- and y-intercepts
x-intercept
The x-intercept is the x-coordinate of the point where the line intersects the x-axis. This happens when the y-coordinate is 0. Then we will evaluate the line equation at y=0 to find the corresponding x value.
The y-intercept is the y-coordinate of the point when the line intersects the y-axis. This happens when the x-coordinate is 0. We will evaluate the line equations at x=0 to find the corresponding y value.
We can use the slope and any of the two points we know to write the line equation in the point-slope form. In this case, we will use the slope value - AB and the point ( CA,0 ).
y - y_1 = m(x- x_1)
y - 0 = - AB ( x - CA )
y = - AB ( x - CA)
We have found the equation in slope-intercept form. Notice that we could have used the other point and obtaining y - CB = - ABx, which is just an equivalent equation to the one we found.
