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