This is a free lesson from our course in Algebra I
This lesson explains how to write the equation of a line if you know its slope
and a point on it. This form of equation of a line is called the point-slope form.
As you'll see, equation of a line with slope m and passing through a point (a, b)
is given by y
- b = m(x - a) Somewhere, you'll find a point as (x1, y1) and a slope m, and a formula:
y – y1 = m(x – x1)
Here subscripts are just intended to indicate the point given.
You have the generic "x" and generic "y" that are always in your equation, and then you have the specific x and y
from the point given; the specific x and y are what is subscripted in the formula. (More text below video...)
(Continued from above) For example : Find the equation of the straight line that has slope m = 4 and passes through the point (1,1).
You've given m = 4, x1 = 1, and y1 = 1.
You'll plug these values into the point-slope form, and solve for "y=":
y – y1 = m(x – x1)
y – (1) = (4)(x – (1))
y -1 = 4(x - 1)
y - 1 = 4x - 4
y = 4x - 4 + 1
y = 4x – 3
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