Writing Linear Equations
Writing linear equations for a graph.
If the graph is nonvertical:
• Determine the y intercept ( b)
• Determine the slope using rise over run (m )
• Write a linear equation using y = mx + b and replacing
m and b with the values you found
If the graph is vertical:
• Determine the x intercept ( a )
• Write a linear equation using x = a and replacing a
with the value you found
Writing a linear equation for a given point and slope.
Example
Write a linear equation with a slope of 2 and containing the
point (3, 5).
Use the pointslope form for a linear equation: y  y_{ 1}
= m ( x  x_{ 1} )
Substitute the values into the equation as follows: y  5 = 2(
x  (3))
y  5 = 2 x + 6
y = 2 x + 11
Writing a linear equation with 2 given points:
Example
Given (0, 2) and (4, 5), write a linear equation
First determine the slope of the line:
Then use the pointslope form to write the equation. Use
either point.
Writing a Linear Equation for a graph described by a 2nd
equation.
• In all cases, find the slope and a point on the line to
solve.
Example
A line passes through the point (3, 2) and has the same slope
as the the line for y = 2x + 5.
m = 2 for both lines so...
y  2 = 2( x  3)
y  2 = 2x + 6
y = 2 x + 8
Example
A line passes through the point (4, 2) and is parallel to
the line 2 x + 4 y = 4.
Find the slope of the line 2 x + 4 y = 4
4 y = 2 x + 4
therefore
Example
A line passes through the point (2, 5) and is perpendicular to
the line  x + 3 y = 2.
Find the slope of the line  x + 3 y = 2.
3 y = x  2
If the slope of  x + 3 y = 2 is
then the slope of the perpendicular is 3 so...
y  5 = 3( x  2)
y  5 = 3 x + 6
y = 3 x + 11
