Writing Linear Equations Given
Two Points On the Line
Using the "Slope – Intercept" Form
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Getting Started
Any two points will determine a line
The line connecting these two points has an equation that describes this line.
Our job is to find this equation when we are only given two points. We will
be using the slope – intercept form of a linear equation
y = mx + b,
and the point – slope form of a linear equation.
y – y1 = m(x – x1)
Using the Slope – Intercept Form
First, let's review the slope – intercept form of a linear equation.
y = mx + b,
(x , y) are ordered pairs that lie on the line
m is the slope of the line
b is the y – intercept (or where the line crosses the y – axis)
Using the Slope – Intercept Form
There are 3 steps involved in writing the equation of a line in
slope – intercept form when we are given two points.
STEP 1: Use the two points to find the
slope of the line
(x1 , y1) and (x2 , y2)
slope = m =
y2 - y1
x2 - x1
STEP 2: Use the slope and ONE of the
points to find the y – intercept
Use y = mx + b. Substitute the
value of m from step 1 and
substitute either one of the points
(x , y). Then solve the equation
for b
STEP 3: Use the slope and y – intercept
to write the equation of the line
Write y = mx + b, but replace the
m and b with the values obtained
from steps 1 and 2.
Using the Slope – Intercept Form
PROBLEM: Write the equation of a line in slope – intercept form that
passes through the points (2 , –3) and (–3 , 7)
STEP 1: Use the two points to find the
slope of the line
So, m = –2
STEP 2: Use the slope and ONE of the
points to find the y – intercept
So, b = 1
STEP 3: Use the slope and y – intercept
to write the equation of the line
y = mx + b
SOLUTION: y = –2x + 1
y2 - y1 7 - (- 3) 10
m=
=
=
=- 2
x2 - x1
- 3- 2
- 5
NEATLY
Pick either of the points. Suppose
we pick the point (2 , –3).
Substitute the x and y values along
with the m value from step 1 into
the equation y = mx + b.
SHOW
YOUR
–3 = (–2)(2) + b
Solve this equation for b.
–3 = –4 + b
WORK
1=b