Download Slope-Intercept Form

4.5 quick
graphs using
slope-intercept
form, pointslope form, &
standard form
Algebra 1
Objectives




Graph a line given any linear
equation.
Understand and use slopeintercept form.
Understand and use the standard
form of an equation.
Understand and use point-slope
form of an equation.
We have used 3 different methods
for graphing equations.
1) Using slope-intercept form.
2) Using x- and y-intercepts.
3) Using point-slope form.
What form is used to graph x- and yintercepts?
The goal is to determine which method is
the easiest to use for each problem!
Various Forms of an Equation
y  mx  b
of a Line.
Slope-Intercept
Form
Standard Form
m  slope of the line
b  y  intercept
Ax  By  C
A, B, and C are integers
A  0, A must be postive
y  y1  m  x  x1 
Point-Slope Form
m  slope of the line
 x1 ,
y1  is any point
Here’s your cheat sheet:



If the equation is in STANDARD FORM,
graph using the intercepts.
If the equation is in SLOPE-INTERCEPT
FORM, graph using slope and intercept
or a t-table (whichever is easier for
you).
If the equation is in neither form,
choose the method you like the best!
6
4.5 Slope Intercept Form
TELEPHONE COSTS
In a community, the monthly cost of
local telephone service
is $5 per month, plus 25¢ per call.
a. Write a linear equation that gives the cost
c for a. person making n calls.
b. Then graph the equation. (need 2 points)
c. Use the graph to estimate the cost of
service in a month when 20 calls
were made.
c = 5 + .25n
Slope-Intercept Form
y = mx + b
slope
rise
run
y-intercept
where the line crosses
the y axis
Slope-Intercept Form:
A linear equation written in the form y = mx + b is in
slope-intercept form.
The slope is m and the y-intercept is (0, b).
To graph an equation in slope-intercept form:
1. Write the equation in the form y = mx + b. Identify m and b.
2. Plot the y-intercept (0, b).
3. Starting at the y-intercept, find another point on the line
using the slope.
4. Draw the line through (0, b) and the point located using the
slope.
9
Slope-Intercept Form
Example: Graph the line y = 2x – 4.
1. The equation y = 2x – 4 is in the
slope-intercept form. So, m = 2 and b = - 4.
y
2. Plot the y-intercept, (0, - 4).
3. The slope is 2. m =
change in y
change in x
x
2
=
1
(1, -2)
2
4. Start at the point (0, 4).
Count 1 unit to the right and 2 units up
to locate a second point on the line.
The point (1, -2) is also on the line.
5. Draw the line through (0, 4) and (1, -2).
(0, - 4)
1
Which graphing method is easiest?


Since the equation is already in slopeintercept form, use slope and the yintercept!
Graph using m and b
1
m=
,b=2
3
2. Graph


-2x + 3y = 12
Which graphing method is
easiest?
Using x- and y-intercepts!
(The equation is in standard
form)
Remember, plug in 0 to find
the intercepts.
Standard Form:
Graphing with intercepts:
-2x + 3y = 12
1.
2.

Find your x-intercept:
Let y = 0
-2x + 3(0) = 12
x = -6; (-6, 0)
Find your y-intercept:
Let x = 0
-2(0) + 3y = 12
y = 4; (0, 4)
Graph both points and draw a line through them.
Which method is easiest to graph
-3x + 6y = 2?
1.
2.
3.
4.
T-table
Slope and intercept
X- and Y-intercepts
Graphing calculator
Explain.
14
Point-Slope Form:
A linear equation written in the form y – y1 = m(x – x1)
is in point-slope form.
The graph of this equation is a line with slope m
passing through the point (x1, y1).
y
Example:
The graph of the equation
y – 3 = - 1 (x – 4) is a line
2
1
8
m=4
of slope m = - passing
1
2
(4, 3)
2
through the point (4, 3).
x
4
8
15
Point-Slope Form
Write the slope-intercept form for the equation of the
line through the points (4, 3) and (-2, 5).
m= 5–3 =- 2 =- 1
-2 – 4
6
3
Calculate the slope.
y – y1 = m(x – x1)
Point-slope form
1
y – 3 = - (x – 4)
3
y = - 1 x + 13
3
3
1
Use m = - and the point (4, 3).
3
Slope-intercept form
16
Point-Slope Form
Example: Write the slope-intercept form for the equation of
the line through the point (-2, 5) with a slope of 3.
Use the point-slope form, y – y1 = m(x – x1), with m = 3 and
(x1, y1) = (-2, 5).
y – y1 = m(x – x1)
Point-slope form
y – y1 = 3(x – x1)
Let m = 3.
y – 5 = 3(x – (-2))
Let (x1, y1) = (-2, 5).
y – 5 = 3(x + 2)
Simplify.
y = 3x + 11
Slope-intercept form
Which is the graph of y = x + 2?
1. .
2. .
3. .
4. .
1. On the next few slides are
some practice problems.
2. Choose which method is
easiest first. Then solve and
graph the equation.
3. Let’s Graph the following
equations 
y  3x  2
2x  3y  0
4x  y  5
7x  3y  4
1
y 3  x
4
5x  2  y
 2 x  3 y  12
yx3
y  6 x
y  2x 1
We have used 3 different methods
for graphing equations.
1) Using slope-intercept form.
2) Using x- and y-intercepts.
3) Using point-slope form.
What form is used to graph xand y-intercepts?
What form is used when the
slope is given with one point?
Linear Equation Review:
Slope-Intercept
Form
Standard Form
y  mx  b
m  slope of the line
b  y  intercept
Ax  By  C
A, B, and C are integers
A  0, A must be postive
y  y1  m  x  x1 
Point-Slope Form
m  slope of the line
 x1 ,
y1  is any point
Chapter 4 Test 
Wednesday, November
20th
 Chapter
4 Test Review Tuesday,
November 19th
 Chapter 4 Study Guide due Tuesday,
November 19th