# 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 point-slope 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 point-slope 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 |