Writing Linear Equations Given Two Points On the Line

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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)
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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)
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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.
(x1 , y1) and (x2 , y2)
STEP 1 Use the two points to find the slope of
the line
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 2 Use the slope and ONE of the points to
find the y intercept
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.
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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
NEATLY SHOW YOUR WORK
So, m 2
Pick either of the points. Suppose we pick the
point (2 , 3).
STEP 2 Use the slope and ONE of the points to
find the y intercept
Substitute the x and y values along with the m
value from step 1 into the equation y mx b.
So, b 1
STEP 3 Use the slope and y intercept to write
the equation of the line
3 (2)(2) b
Solve this equation for b.
y mx b y 2x 1
3 4 b 1 b
SOLUTION