4.5: Equations of Lines from Graphs
Write the equation, in standard form, of the following graph:
Watch This
Khan Academy Slope and yIntercept Intuition
Guidance
You can determine the equation of a line from a graph by counting. Find the yintercept (
The
If you cannot determine the yintercept, you can algebraically determine the equation of a line by using the coordinates of two points on the graph. These two points can be used to calculate the slope of the line by counting and then the yintercept can then be determined algebraically.
To write the equation of a line in standard form, the value of the
Example A
Determine the equation of the following graph. Write the equation in slopeintercept form.
Solution:
The
Example B
Determine the equation, in slopeintercept form of the line shown on the following graph:
Solution:
The
The equation in slopeintercept form is
Example C
Determine the equation, in standard form, for the line on the following graph:
Solution:
The
The equation of the line in standard form is
Concept Problem Revisited
Write the equation, in standard form, of the following graph:
The first step is to determine the slope of the line.

The slope of the line is
34 . The coordinates of one point on the line are (2, 5). 
y−y1y−5y−54(y)−4(5)4(y)−4(5)4y−20−3x+4y−20−3x+4y−20−3x+4y−20+6−3x+4y−143x−4y+14=m(x−x1)=34(x−2)=34x−64=4(34)x−4(64)=4(34)x−4(64)=3x−6=3x−3x−6=−6=−6+6=0=0
The equation of the line in standard form is
Vocabulary
 Slope – Intercept Form

The slopeintercept form is one method for writing the equation of a line. The slopeintercept form is
y=mx+b wherem refers to the slope andb identifies they intercept.
 Standard Form

The standard form is another method for writing the equation of a line. The standard form is
Ax+By+C=0 whereA is the coefficient ofx ,B is the coefficient ofy andC is a constant.
Guided Practice
1. Write the equation, in slopeintercept form, of the following graph:
2. Write the equation, in slopeintercept form, of the following graph:
3. Rewrite the equation of the line from #2 in standard form.
Answers:
1. The first step is to determine the coordinates of the

The
y intercept is (0, 3) sob=−3 . The second step is to count to determine the value of the slope. The slope is47 . The equation of the line in slopeintercept form isy=47x−3
2. The

The coordinates of two points on the line are (1, 0) and (6, 4). The slope is is
−45 . They intercept of the line must be calculated by using the slope and one of the points on the line. 
y000+4545=mx+b=−45(1)+b=−45+b=−45+45+b=b
The equation of the line in slopeintercept form is
3. To rewrite the equation in standard form, first multiply the equation by 5 to get rid of the fractions. Then, set the equation equal to 0.

y5y4x+5y−4=−45x+45=−4x+4=0
Practice
For each of the following graphs, write the equation in slopeintercept form:
For each of the following graphs, write the equation in slopeintercept form:
For each of the following graphs, write the equation standard form:
Image Attributions
Description
Learning Objectives
Here you'll learn how to find the equation of a line from its graph.
Difficulty Level:
At GradeSubjects:
Date Created:
Dec 19, 2012Last Modified:
Apr 29, 2014Vocabulary
If you would like to associate files with this Modality, please make a copy first.