Section 3.2 Graphing Linear Equations Using Intercepts
Definition:
x–intercept: the point where the line crosses (or intercepts) the x-axis
y–intercept: : the point where the line crosses (or intercepts) the y-axis
y-int: (0, y)
x-int: (x, 0)
Types of Linear:
Positive Slope
Negative Slope
Slope = 0: y=b
Undefined slope: x=a
Steps for graphing a Linear Equation in Two Variables
 Step 1. Find x-intercept and y-intercept by substituting x = 0 and y = 0
 Step 2. Plot intercepts obtained in the step 1
 Step 3: Draw a line through these two points
Cheon-Sig Lee
Page 1
Section 3.2 Graphing Linear Equations Using Intercepts
Example
Plot intercepts to graph the
equation: 𝑦 = 2𝑥 + 4
(Solution)
Step 1: Find intercepts
y-intercept: (0, y)
𝑦= 2𝑥 + 4
= 2(0) + 4
=4
Thus, y-int: (0, 4)
x-intercept: (x, 0)
𝑦= 2𝑥 + 4
0= 2𝑥 + 4
−4
−4
−4= 2𝑥
−4 2𝑥
=
2
2
−2= 𝑥
Thus, x-int: (–2, 0)
12
10
8
6
4
2
0
-12 -10
-8
-6
-4
-2
-2
0
2
4
6
8
10
12
-4
-6
-8
-10
-12
Step 2: Plot intercept obtained in the step 2, (0, 4) and (–2, 0)
Step 3: Draw a line through these two points, (0, 4) and (–2, 0)
TI-83/84:
2nd WINDOW > Y= > 2X +4 > 2nd MODE > 2nd GRAPH
x-int: (-2, 0)
y-int: (0, 4)
2nd WINDOW
TI-89:
F4 > tblStart: -10 / ∆tbl: 0.5 >
Cheon-Sig Lee
2nd GRAPH
F1 > 2X+4 > 2nd F5
Page 2
Section 3.2 Graphing Linear Equations Using Intercepts
Excercise
(Solution 1)
x-intercept is the point where the graph intercepts the x-axis. The given graph crosses at 2 on the x-axis.
y-intercept is the point where a line crosses the y-axis. The given graph crosses at 7 on the y-axis.
(Solution 2)
x-intercept is the point where the graph intercepts the x-axis. The horizontal line does not cross the x-axis.
y-intercept is the point where a line crosses the y-axis. The given graph crosses at – 4 on the y-axis.
Cheon-Sig Lee
Page 3
Section 3.2 Graphing Linear Equations Using Intercepts
(Solution 3)
x-intercept is the point where the graph intercepts the x-axis. The horizontal line does not cross the x-axis.
y-intercept is the point where a line crosses the y-axis. The given graph crosses at 7 on the y-axis.
(Solution 4)
Step 1: Find x-intercept
Substitute y = 0
𝑥 + 𝑦= 7
𝑥 + (0)= 7
𝑥= 7
So, x-intercept is (7, 0)
Step 2: Find y-intercept
Substitute x = 0
𝑥 + 𝑦= 7
(0) + 𝑦= 7
𝑦= 7
So, y-intercept is (0, 7)
Step 3: Plot the obtained points.
The graph is shown below
Cheon-Sig Lee
Page 4
Section 3.2 Graphing Linear Equations Using Intercepts
(Solution 5)
Step 1: Find x-intercept
Substitute y = 0
7𝑥 − 3𝑦= −21
7𝑥 − 3(0)= −21
7𝑥 = −21
7𝑥 −21
=
7
7
𝑥 = −3
So, x-intercept is (–3, 0)
Step 2: Find y-intercept
Substitute x = 0
7𝑥 − 3𝑦= −21
7(0) − 3𝑦= −21
−3𝑦= −21
−3𝑦 −21
=
−3
−3
𝑦= 7
So, y-intercept is (0, 7)
Step 3: Plot the obtained points.
The graph is shown below.
(Solution 6)
Step 1: Find x-intercept
Substitute y = 0
45𝑦= 360 − 180𝑥
45(0)= 360 − 180𝑥
0= 360 − 180𝑥
−360 −360
−360= −180𝑥
−360 −180𝑥
=
−180 −180
2= 𝑥
So, x-intercept is (2, 0)
Step 2: Find y-intercept
Substitute x = 0
45𝑦= 360 − 180𝑥
45𝑦= 360 − 180(0)
45𝑦= 360
45𝑦 360
=
45
45
𝑦= 8
So, y-intercept is (0, 8)
Step 3: Plot the obtained points.
The graph is shown below
Cheon-Sig Lee
Page 5
Section 3.2 Graphing Linear Equations Using Intercepts
(Solution 7)
Step 1: Find x-intercept
Substitute y = 0
4𝑥 − 8𝑦= 28
4𝑥 − 8(0)= 28
4𝑥 = 28
4𝑥 28
=
4
4
𝑥= 7
So, x-intercept is (7, 0)
Step 2: Find y-intercept
Substitute x = 0
4𝑥 − 8𝑦= 28
4(0) − 8𝑦= 28
−8𝑦= 28
−8𝑦 28
=
−8 −8
𝑦= −3.5
So, y-intercept is (0, −3.5)
Step 3: Plot the obtained points. The graph is shown below.
(Solution 8)
Step 1: Find x-intercept
Substitute y = 0
𝑥 + 𝑦= 6
𝑥 + (0)= 6
𝑥= 6
So, x-intercept is (6, 0)
Step 2: Find y-intercept
Substitute x = 0
𝑥 + 𝑦= 6
(0) + 𝑦= 6
𝑦= 6
So, y-intercept is (0, 6)
Step 3: Plot the obtained points. The graph is shown below.
Cheon-Sig Lee
Page 6
Section 3.2 Graphing Linear Equations Using Intercepts
(Solution 9)
Step 1: Find x-intercept
Substitute y = 0
9𝑥 − 3𝑦= 9
9𝑥 − 3(0)= 9
9𝑥 = 9
9𝑥 9
=
9 9
𝑥= 1
So, x-intercept is (1, 0)
Step 2: Find y-intercept
Substitute x = 0
9𝑥 − 3𝑦= 9
9(0) − 3𝑦= 9
−3𝑦= 9
−3𝑦 9
=
−3 −3
𝑦= −3
So, y-intercept is (0, –3)
Step 3: Plot the obtained points. The graph is shown below.
(Solution 10)
A horizontal line is given by y = b, where b is the y-intercept.
The y-intercept, b, is the y-coordinate of the point at which the
graph crosses or touches the y-axis.
Since the graph intercepts at 5 on y-axis, b =5
Therefore, the equation for the line is y = 5.
(Solution 10)
A vertical line is given by x = a, where a is the x-intercept.
The x-intercept, a, is the x-coordinate of the point at which the
graph crosses or touches the x-axis.
Since the graph intercepts at – 4 on x-axis, a = –4
Therefore, the equation for the line is x = –4.
Cheon-Sig Lee
Page 7