Writing Linear Equations in SlopeIntercept Form
Objective Learn the slopeintercept form of
the equation defining a line.
The slopeintercept form is an extremely useful special case
of the pointslope form of the equation defining a straight line.
It is written as y = mx + b, where m is the slope and b is the yintercept,
the point where the line intersects the yaxis. The x and yintercepts
of a line are the points where the line intersects the x and yaxes,
respectively.
First, we will try to answer the question “How can we
determine the x and yintercepts of a line that is given in the
form of an equation?”
Then we will learn how to find the intercepts algebraically by
solving linear equations. This can be done whether the equations
are in standard form or in pointslope form.
Example 1
Find the yintercept of the graph of 2x + 3y = 12.
Solution
This equation is in standard form. The yintercept is the
intersection of the line and the yaxis, so it is a point that is
both on the line and on the yaxis. It satisfies the following
equations.
2x + 3y 
= 12 
Equation of the line 
x 
= 0 
Equation of the yaxis 
To find the yintercept, let x = 0 in the equation of the
line.
2x + 3y 
= 12 

2(0) + 3y 
= 12 
Let x = 0. 
3y 
= 12 

y 
= 4 
Divide each side by 3. 
The yintercept of this line is 4, so the line crosses the
yaxis at (0, 4).
Example 2
Find the yintercept of the graph of 2( y  1) = 5( x + 2).
Solution
This equation is in pointslope form. As in the case of
standard form, let x = 0 and solve for y.
2( y  1) 
= 5( x + 2) 

2( y  1) 
= 5( 0 + 2) 
Let x = 0. 
2y  2 
= 10 
Distributive Property 
2y 
= 12 
Add 2 to each side. 
y 
= 6 
Divide each side by 2. 
So, the yintercept is 6 and the line crosses the yaxis at
(0, 6).
To find the xintercept, let y = 0 in the equation, since the
xaxis is given by the equation y = 0. Practice finding the x and
yintercepts of the graphs of equations.
