Writing Linear Equations in SlopeIntercept Form
SlopeIntercept Form
The slopeintercept form is a special case of the pointslope
form. The given point of the line (x_{ 0} , y_{ 0}
) lies on the yaxis, so x_{0} = 0. This means that the
equation is of the form y  y_{ 0} = mx, or y = mx + y_{
0} . The equation is therefore given explicitly when both
the yintercept and the slope are known, and is simpler than the
more general pointslope form. This is perhaps the most common
and most important normal form for the equation of a line.
Example 1
Write the slopeintercept form of the equation for a line that
goes through (0, 4) and has a slope of 5.
Solution
y  y_{ 0} 
= m ( x  x_{ 0} ) 
Pointslope form 
y  4 
= 5x 
Replace x_{ 0} with 0, y_{ 0}
with 4, and m with 5. 
Now add 4 to each side of this equation in order to express y
in terms of x . The result is the following equation.
y = 5 x + 4
Point out that 5 is the slope of the line and that 4 is the
yintercept.
Example 2
Write the slopeintercept form of the equation for a line that
goes through (0, 3) and has a slope of 1.
Solution
y  y_{ 0} 
= m ( x  x_{ 0} ) 
Pointslope form 
y  ( 3) 
= ( 1)x 
Replace x_{ 0} with 0, y_{ 0}
with 3 , and m with 1. 
y + 3 
= x 

Now subtract 3 from each side of this equation in order to
express y in terms of x . The result is the following equation.
y = x  3
Point out that 1 is the slope of the line and that 3 is the
y intercept.
Notice that these equations are really much simpler than the
general pointslope form, since there are fewer terms. Also note
that in each case, the coefficient of x is the slope and the
constant term is the yintercept.
Key Idea An equation for a line is in
slopeintercept form if it is of the form y = mx + b, where m is
the slope of the line and b is the yintercept.
Any line that is not vertical has an equation that is in
slopeintercept form. A vertical line could not possibly have an
equation in slopeintercept form, for the same reason that it
cannot have an equation in pointslope form  the slope is
undefined.
