Give the equation of a line with a known slope and point
The slope-intercept form has the advantage of being simple to remember and use, however, it has one major disadvantage: we must know the y-intercept in order to use it! Generally we do not know the y-intercept, we only know one or more points (that are not the y-intercept). In these cases we can’t use the slope intercept equation, so we will use a diﬀerent more ﬂexible formula. If we let the slope of an equation be m, and a speciﬁc point on the line be , and any other point on the line be (x, y). We can use the slope formula to make a second equation.
Find the equation on the line and any other point on the line be (x,y)
Recall slope formula
Plug in value
Multiply both sides by
So, the solution is
If we know the slope, m of an equation and any point on the line we can easily plug these values into the equation above which will be called the point- slope formula.
Point –Slope Formula:
Write the equation of the line through the point (3, -4) with a slope of
Plug values into point – slope formula
Simplify signs, and the solution is
Often, we will prefer final answers be written in slope intercept form. If the directions ask for the answer in slope-intercept form we will simply distribute the slope, then solve for y.
Write the equation of the line through the point ( – 6, 2) with a slope of in slope-intercept form.
Plug values into point -slope formula
Solve for y
Add +2 to both sides
And the solution is:
An important thing to observe about the point slope formula is that the operation between the x’s and y’s is subtraction. This means when you simplify the signs you will have the opposite of the numbers in the point. We need to be very careful with signs as we use the point-slope formula.
In order to find the equation of a line we will always need to know the slope. If we don’t know the slope to begin with we will have to do some work to find it first before we can get an equation.
Find the equation of the line through the points ( -2, 5) and (4, -3).
First we must find the slope
Plug values in slope formula and evaluate
With slope and either point, use point -slope formula
Simplify signs and the solutions is