Linear Functions
Review of Formulas
Formula for Slope
y2  y1
m
x 2  x1
Standard Form
Ax  By  C
*where A>0 and A, B, C are integers
Slope-intercept Form
Point-Slope Form
y  mx  b
y  y1  mx  x1 
Find the slope of a line through
points (3, 4) and (-1, 6).
1
64
2

m

2
1 3
4
3
Change y  x  2 into
4
standard form.
3
4 y  4 x 42
4
3x  4y  8
3x  4y  8
Change 3x  5y 15 into slopeintercept form and identify the
slope and y-intercept.
5y  3x 15
5y 3x 15


5
5 5
3
3
y  x  3 m  5 and b  5
5
Write an equation for the line that
passes through (-2, 5) and (1, 7):
75 2

Find the slope: m 
12 3
Use pointslope form:
2
y  5  x  2 
3
x-intercepts and y-intercepts
The intercept is the point(s)
where the graph crosses the axis.
To find an intercept, set the other
variable equal to zero.
3x  5y 15
3x  50 15
3x  15
x 5
 5, 0  is the
x -intercept
Horizontal Lines
 Slope is zero.
 Equation form is y = #.
Write an equation of a line and graph it
with zero slope and y-intercept of -2.
y = -2
Write an equation of a line and graph it
that passes through (2, 4) and (-3, 4).
y=4
Vertical Lines
 Slope is undefined.
 Equation form is x = #.
Write an equation of a line and graph it
with undefined slope and passes
through (1, 0).
x=1
Write an equation of a line that passes
through (3, 5) and (3, -2).
x=3
Graphing Lines
*You need at
least 2 points to
graph a line.
Using x and y intercepts:
•Find the x and y intercepts
•Plot the points
•Draw your line
Graph using x and y intercepts
2x – 3y = -12
x-intercept
2x = -12
x = -6
(-6, 0)
y-intercept
-3y = -12
y=4
(0, 4)
6
B: ( 0 , 4 )
4
B
2
A: ( -6 , 0 )
-10
A -5
-2
Graph using x and y intercepts
6x + 9y = 18
x-intercept
6x = 18
x=3
(3, 0)
y-intercept
9y = 18
y=2
(0, 2)
4
D: ( 0 , 2 )
2
D
C: ( 3 , 0 )
C
-2
5
Graphing Lines
Using slope-intercept form y = mx + b:
•Change the equation to y = mx + b.
•Plot the y-intercept.
•Use the numerator of the slope to count the
corresponding number of spaces up/down.
•Use the denominator of the slope to count
the corresponding number of spaces left/right.
•Draw your line.
Graph using slope-intercept form
y = -4x + 1:
Slope
m = -4 = -4
1
4
2
E: ( 0 , 1 )
E
5
y-intercept
(0, 1)
-2
F: ( 1 , -3 )
F
-4
Graph using slope-intercept form
3x - 4y = 8
y = 3x - 2
4
4
2
G: ( 4 , 1 )
G
Slope
m=3
4
5
y-intercept
(0, -2)
-2
H
-4
H: ( 0 , -2 )
Parallel Lines
**Parallel lines have the same slopes.
•Find the slope of the original line.
•Use that slope to graph your new line
and to write the equation of your new
line.
Graph a line parallel to the given
line and through point (0, -1):
2
5
3
-2
-4
5
Slope = 3
5
Write the equation of a line parallel to
2x – 4y = 8 and containing (-1, 4):
– 4y = - 2x + 8
y = 1x - 2
2
Slope = 1
2
y  y1  mx  x1 
y - 4 = 1(x + 1)
2
Perpendicular Lines
**Perpendicular lines have the
opposite reciprocal slopes.
•Find the slope of the original line.
•Change the sign and invert the
numerator and denominator
of the slope.
•Use that slope to graph your new
line and to write the equation
of your new line.
Graph a line perpendicular to the
given line and through point (1, 0):
Slope =-3
4
4
4
2
-3
Perpendicular
5
-2
Slope= 4
3
Write the equation of a line
perpendicular to
y = -2x + 3 and containing (3, 7):
Original Slope= -2
Perpendicular
Slope = 1
2
y  y1  mx  x1 
y - 7 = 1(x - 3)
2
Write the equation of a line
perpendicular to
3x – 4y = 8 and containing (-1, 4):
-4y = -3x + 8
3
y  x2
4
Slope= 3
4
Perpendicular
Slope = -4
3
y  y1  mx  x1 
y - 4 = -4(x + 1)
3