Transcript 4.6 Quick Graphs Using Slope-Intercept Form

Quick Graphs Using SlopeIntercept Form
4.6
GOAL
1
Graphing Using Slope-Intercept Form
SLOPE-INTERCEPT FORM OF A LINEAR EQUATION
The equation of a line with slope m and y-intercept b is:
y = mx + b
EXAMPLE 1
Extra Example 1
Write the equation 3x + 4y = 8 in slope-intercept form. Then
identify the slope and the y-intercept.
3x + 4y = 8
Solve for y:
3
slope  
4
3
y   x2
4
y-intercept = 2
To graph a line using its slope and y-intercept, first plot the
y-intercept, and then use the slope to graph at least one
other point.
EXAMPLE 2
Extra Example 2
y
Graph 2x + y = 5.
(0, 5)
First, write in slopeintercept form:
y = –2x + 5
x
Next, identify and
plot the y-intercept:
b=5
Now use the slope to
find another point and
draw a line through the
points:
rise 2
m

run 1
Two different lines in the same plane that do not intersect
are _______.
parallel
In the coordinate plane, two vertical lines are parallel.
Two nonvertical lines are parallel if and only if they have
the same ______.
slope
EXAMPLE 3
Extra Example 3
Which of the following lines are parallel?
a. 3y = –9x – 5
b. 2y – 6x = –5
c. 12x + 4y = 1
Write each equation in slope-intercept form to determine
their slopes:
5
a. y  3x 
3
m  3
5
b. y  3x 
2
1
c. y  3x 
4
m3
Since equations a and c have the
same slopes, they are parallel.
m  3
Checkpoint
Are the lines –2x + y = 5 and 4y = 8x – 1 parallel?
Since each line has a slope of 2,
they are parallel.
4.6
GOAL
Quick Graphs Using SlopeIntercept Form
2
SOLVING REAL-LIFE PROBLEMS
EXAMPLE 4
Extra Example 4
The equations below model the changing speeds of a car as
it enters an expressway, travels on the expressway, and then
exits the expressway. Create a graph to represent the car’s
different speeds.
Stage 1 (first 2 minutes): s = 15t + 25
Domain: 0 ≤ t < 2
Stage 2 (next 10 minutes): s = 55
Domain: 2 ≤ t < 12
Stage 3 (next 2 minutes): s = –15t + 235 Domain: 12 ≤ t < 14
Extra Example 4 (cont.)
Speed (mi/h)
Stage 1 (first 2 minutes): s = 15t + 25
Domain: 0 ≤ t < 2
Stage 2 (next 10 minutes): s = 55
Domain: 2 ≤ t < 12
Stage 3 (next 2 minutes): s = –15t + 235 Domain: 12 ≤ t < 14
(12, 55)
60 (2, 55)
50
40
30
(14, 25)
20 (0, 25)
10
0
0 2 4 6 8 10 12 14
Time (min)
Checkpoint
Graph each line for the given domain on the same
coordinate axes.
a. y = 2x + 10
Domain: –5 ≤ x < –3
b. y = 4
Domain: –3 ≤ x < –1
c. y = –4x
Domain: –1 ≤ x < 0
y
x