Graphs to Linear Equations Sample Problems

Math Practice Online > free > lessons > New York > 9th grade > Graphs to Linear Equations

If your child needs math practice, click here.

For sample problems, click here.
Here are some tips for Graphs to Linear Equations, which aligns with New York state standards:

Graphs to Linear Equations

For this topic, you need to know how to find the slope of a line from its graph.
To review the Determining Slope topic, see here.

In this topic, you will find the equation of a line based on its graph.
One way to write an equation for a straight line is the slope-intercept form:

y = mx + b where m is the slope and b is the y-intercept

The y-intercept is the point (0, b) on the line, or the point where the line passes through the y-axis.

To find the equation of a line, follow these steps:

Find the slope of the line, m.
Find the y-intercept of the line, b.
Plug m and b into the equation y = mx + b.

Example 1: Horizontal and Vertical Lines

Write the equation that represents this line. Examples: y=3x/4, x=2, y=1, y=2x

Horizontal Line Vertical Line

A horizontal line has zero slope, m = 0.
Horizontal lines have equations like y = b.
For this line, the line crosses the y-axis at (0, 5).
The y-intercept of the line is 5.
The equation for the line is
A vertical line has an undefined slope, m doesn't exist.
Vertical lines have equations like x = c.
There is no y-intercept for this line because it does not cross the y-axis.
The equation for the line is

Horizontal Line	Vertical Line

A horizontal line has zero slope, m = 0. Horizontal lines have equations like y = b. For this line, the line crosses the y-axis at (0, 5). The y-intercept of the line is 5. The equation for the line is	A vertical line has an undefined slope, m doesn't exist. Vertical lines have equations like x = c. There is no y-intercept for this line because it does not cross the y-axis. The equation for the line is

Example 2: y = mx + b

Write the equation in y=mx+b format.

Step 1: Find the slope, m.
Let's pick the two points (0, 4) and (4, 1) on the line to find the slope.

m = 4 - 1
0 - 4 = 3
-4

Step 2: Find the y-intercept, b.
The line crosses the y-axis at point (0, 4) so the y-intercept is 4.
Step 3: Put m and b in the equation.

y = mx + b

y = -3
4 x + 4

The answer is .