Main Idea and New Vocabulary
NGSSS
Example 1: Find Slopes and y-intercepts
Example 2: Find Slopes and y-intercepts
Example 3: Write an Equation in Slope-Intercept Form
Example 4: Write an Equation in Slope-Intercept Form
Example 5: Graph Using Slope-Intercept Form
Example 6: Graph an Equation to Solve Problems
Example 7: Graph an Equation to Solve Problems
Five-Minute Check
• Graph linear equations using the slope and
y-intercept.
• slope-intercept form
• y-intercept
MA.8.A.1.2 Interpret the slope and the x- and
y-intercepts when graphing a linear
equation for a real-world problem.
Find Slopes and y-intercepts
State the slope and y-intercept of the graph of
y=
x – 5.
Write the equation in the form y = mx + b.
Answer: The slope of the graph is
y-intercept is −5.
, and the
State the slope and y-intercept of the graph of
.
A. slope:
B. slope:
; y-intercept: 1
; y-intercept: 1
C. slope: 1; y-intercept:
D. slope: 1; y-intercept:
Find Slopes and y-intercepts
State the slope and y-intercept of the graph of
2x + y = 8.
2x + y = 8
Write the original equation.
2x – 2x + y = 8 – 2x
Subtract 2x from each side.
y = 8 − 2x
Simplify.
y = −2x + 8
Write the equation in the form
y = mx + b.
y = mx + b
m = –2, b = 8
Answer: The slope of the graph is –2 and the
y-intercept is 8.
State the slope and y-intercept of the graph of
y – 4x = 10.
A. slope: –4; y-intercept: 10
B. slope: 4; y-intercept: 10
C. slope: 10; y-intercept: –4
D. slope: 10; y-intercept: 4
Write an Equation in SlopeIntercept Form
Write an equation of a line in slope-intercept form
with a slope of 2 and a y-intercept of –8.
y = mx + b
Slope-intercept form
y = 2x + (–8)
Replace m with 2 and b with –8.
y = 2x – 8
Simplify.
Answer: y = 2x – 8
Write an equation of a line in slope-intercept form
with a slope of –
A. y = –
x–6
B. y = –
x+6
C. y =
x+6
D. y = 6x –
and a y-intercept of 6.
Write an Equation in SlopeIntercept Form
Write an equation in
slope-intercept form
for the graph shown.
The y-intercept is 1. From (0, 1), you move up
2 units and left 3 units to another point on the line.
So, the slope is –
.
Write an Equation in SlopeIntercept Form
y = mx + b
Slope-intercept form
y=– x+1
Replace m with –
y=– x+1
Answer: y = –
x+1
and b with 1.
Write an equation in slope-intercept form for the
graph shown.
A. y = –3x – 2
B. y = 3x – 2
C. y = –
D. y =
x–1
x–1
Graph Using Slope-Intercept Form
Graph
using the slope and
y-intercept.
Step 1 Find the slope and y-intercept.
y=
x+2
slope =
, y-intercept = 2
Graph Using Slope-Intercept Form
Step 2 Graph the y-intercept 2.
Graph Using Slope-Intercept Form
Step 3 Use the slope to locate a second point on the
line.
m=
←change in y: up 2 units
←change in x: right 3 units
Graph Using Slope-Intercept Form
Step 4 Draw a line through the two points.
Answer:
Graph y = –
x + 3 using the slope and y-intercept.
A.
B.
C.
D.
Graph an Equation to Solve
Problems
KAYAK RENTAL A kayak rental pavilion charges
$15.00 per hour and $2.50 for instruction on how
to not fall out of the kayak. The total cost is given
by the equation y = 15x + 2.5, where x is the
number of hours the kayak is rented. Graph the
equation to find the total cost for 2 hours.
y = 15x + 2.5
slope = 15, y-intercept = 2.5
Graph an Equation to Solve
Problems
Plot the point (0, 2.5).
Locate another point up 15
and right 1.
Draw the line.
The y-coordinate is 32.5
when the x-coordinate is 2,
so the total cost for 2 hours
is $32.50.
Answer: The total cost for 2 hours is $32.50.
POTTERY A pottery studio charges $16 per hour
and $10 for firing fees. The total cost is given by
the equation y = 16x + 10, where x is the number
of hours a customer uses the studio. Graph the
equation to find the total cost for 5 hours.
A. $26
B. $80
C. $90
D. $100
Graph an Equation to Solve
Problems
KAYAK RENTAL A kayak rental pavilion charges
$15.00 per hour and $2.50 for instruction on how
to not fall out of the kayak. The total cost is given
by the equation y = 15x + 2.5, where x is the
number of hours the kayak is rented. Interpret the
slope and the y-intercept.
Graph an Equation to Solve
Problems
Answer: The slope 15 represents the rate of change
or cost per hour. The y-intercept 2.5 is the
charge for instruction.
POTTERY A pottery studio charges $16 per hour and
$10 for firing fees. The total cost is given by the
equation y = 16x + 10, where x is the number of hours a
customer uses the studio. Interpret the slope and the
y-intercept.
A.
The slope 10 represents the firing fee.
The y-intercept 16 is the cost per hour.
B.
The slope 10 represents the cost per
hour. The y-intercept 16 is the firing fee.
C.
The slope 16 represents the firing fee.
The y-intercept 10 is the cost per hour.
D.
The slope 16 represents the cost per
hour. The y-intercept 10 is the firing fee.
State the slope and the y-intercept for the graph
of the equation y = 2x + 1.
A. m =
;b=1
B. m = 1; b = 2
C. m = 2; b = –
D. m = 2; b = 1
State the slope and the y-intercept for the graph
of the equation y = 3x + 2.
A. m = –2; b = 3
B. m = 2; b = 3
C. m = 3; b = –2
D. m = 3; b = 2
State the slope and the y-intercept for the graph
of the equation y = −2x + 4.5.
A. m = −4.5; b = –2
B. m = −2; b = 4.5
C. m = 2; b = 4.5
D. m = 4.5; b = –2
State the slope and the y-intercept for the graph
of the equation 3x − y = 4.
A. m = 3; b = −4
B. m = –3; b = −4
C. m = 3; b = 4
D. m = −4; b = 3
The total price of apples y at an orchard can be
calculated with the equation 1.12x + 5 = y, where
x is the number of pounds of apples picked. What
does the slope represent?
A. the total price of apples
B. the price of apples per pound
C. the number of apples per pound
D. the number of pounds of apples picked
What is the equation of the graph?
A. y = 2x –
B. y =
x+2
C. y =
x−2
D. y =
x–2