1. 2.3 Linear Equations
Objectives:
 I will use the slope-intercept form of a
linear equation to graph linear
equations.
 I will use the standard form of a linear
equation to graph linear equations.

2. Identifying a Linear Equation
Ax + By = C
● The exponent of each variable is 1.
● The variables are added or subtracted.
● A or B can equal zero.
● A>0
● Besides x and y, other commonly used variables
are m and n, a and b, and r and s.
● There are no radicals in the equation.
● Every linear equation graphs as a line.

3. Examples of linear equations
2x + 4y =8 Equation is in Ax + By =C form
Rewrite with both variables
6y = 3 – x on left side … x + 6y =3
x=1 B =0 … x + 0 • =1
y
-2a + b = 5 Multiply both sides of the
equation by -1 … 2a – b = -5
4x − y
= −7 Multiply both sides of the
equation by 3 … 4x –y =-21
3

4. Examples of Nonlinear Equations
The following equations are NOT in the
standard form of Ax + By =C:
4x2 + y = 5 The exponent is 2
x=4 There is a radical in the equation
xy + x = 5 Variables are multiplied
s/r + r = 3 Variables are divided

5. x and y -intercepts
● The x-intercept is the point where a line crosses
the x-axis.
The general form of the x-intercept is (x, 0).
The y-coordinate will always be zero.
● The y-intercept is the point where a line crosses
the y-axis.
The general form of the y-intercept is (0, y).
The x-coordinate will always be zero.

6. Finding the x-intercept
● For the equation 2x + y = 6, we know that
y must equal 0. What must x equal?
● Plug in 0 for y and simplify.
2x + 0 = 6
2x = 6
x=3
● So (3, 0) is the x-intercept of the line.

7. Finding the y-intercept
● For the equation 2x + y = 6, we know that x
must equal 0. What must y equal?
● Plug in 0 for x and simplify.
2(0) + y = 6
0+y=6
y=6
● So (0, 6) is the y-intercept of the line.

8. To summarize….
● To find the x-intercept, plug in 0
for y.
● To find the y-intercept, plug in 0
for x.

9. Find the x and y- intercepts
of x = 4y – 5
● x-intercept: ● y-intercept:
● Plug in y = 0 ● Plug in x = 0
x = 4y - 5 x = 4y - 5
x = 4(0) - 5 0 = 4y - 5
x=0-5 5 = 4y
5
x = -5 =y
4
● (-5, 0) is the 5
x-intercept ● (0, 4 )is the
y-intercept

10. Find the x and y-intercepts
of g(x) = -3x – 1*
● x-intercept ● y-intercept
● Plug in y = 0 ● Plug in x = 0
g(x) = -3x - 1 g(x) = -3(0) - 1
0 = -3x - 1 g(x) = 0 - 1
1 = -3x g(x) = -1
1
− ● (0, -1) is the
1 3 =x
● ( − 3 , 0) is the y-intercept
x-intercept
*g(x) is the same as y

11. Find the x and y-intercepts of
6x - 3y =-18
● x-intercept ● y-intercept
● Plug in y = 0 ● Plug in x = 0
6x - 3y = -18 6x -3y = -18
6x -3(0) = -18 6(0) -3y = -18
6x - 0 = -18 0 - 3y = -18
6x = -18 -3y = -18
x = -3 y=6
● (-3, 0) is the ● (0, 6) is the
x-intercept y-intercept

12. Find the x and y-intercepts
of x = 3
● x-intercept ● y-intercept
● Plug in y = 0. ● A vertical line never
crosses the y-axis.
There is no y. Why?
● There is no y-intercept.
●x = 3 is a vertical line
so x always
equals 3.
● (3, 0) is the x-intercept.
x

13. Find the x and y-intercepts
of y = -2
● x-intercept
● y-intercept
● Plug in y = 0.
● y = -2 is a horizontal line
y cannot = 0 because so y always equals -2.
y = -2. ● (0,-2) is the y-intercept.
● y = -2 is a horizontal
x
line so it never crosses
the x-axis.
y
●There is no x-intercept.

14. Graphing Equations
● Example: Graph the equation -5x + y = 2
Solve for y first.
-5x + y = 2 Add 5x to both sides
y = 5x + 2
● The equation y = 5x + 2 is in slope-intercept form,
y = mx+b. The y-intercept is 2 and the slope is 5.
Graph the line on the coordinate plane.

15. Graphing Equations
Graph y = 5x + 2
x
y

16. Graphing Equations
Graph 4x - 3y = 12
● Solve for y first
4x - 3y =12 Subtract 4x from both sides
-3y = -4x + 12 Divide by -3
-4 12
y = -3 x + -3 Simplify
4
y = 3x – 4
4
● The equation y = - 4 is in slope-intercept form,
3x
y=mx+b. The y -intercept is -4 and the slope is 4 .
3
Graph the line on the coordinate plane.

17. Graphing Equations
4
Graph y = 3x -4
x
y