Writing Equations in Slope-Intercept Form
Write an Equation Given Slope and One Point
Write an equation of a line that passes through (2, –3)
with slope
Step 1
The line has slope
replace m with
To find the y-intercept,
and (x, y) with (2, –3) in the
slope-intercept form. Then, solve for b.
Write an Equation Given Slope and One Point
Slope-intercept form
Replace m with
y with –3,
and x with 2.
,
Multiply.
Subtract 1 from each side.
Simplify.
Write an Equation Given Slope and One Point
Step 2
Write the slope-intercept form using
Slope-intercept form
Replace m with
Answer: The equation is
and b with –4.
Write an Equation Given Slope and One Point
Write an equation of a line that passes through (1, 4)
and has a slope of –3.
Answer:
Writing Equations in Slope-Intercept Form
If you are not given the slope but you
know two points on the line, find the slope
first then choose one of the points to find
the y-intercept.
Write an Equation Given Two Points
Multiple-Choice Test Item
x
y
The table of ordered pairs shows
the coordinates of two points on the
graph of a function. Which equation
describes the function?
–3
–4
–2
–8
A
B
C
D
Read the Test Item
The table represents the ordered pairs (–3, –4)
and (–2, –8).
Write an Equation Given Two Points
Solve the Test Item
Step 1 Find the slope of the line containing the points.
Let
and
Slope formula
Simplify.
.
Write an Equation Given Two Points
Step 2 You know the slope and two points. Choose one
point and find the y-intercept. In this case, we
chose (–3, –4).
Slope-intercept form
Replace m with –4,
x with –3, and y with –4.
Multiply.
Subtract 12 from
each side.
Simplify.
Write an Equation Given Two Points
Step 3 Write the slope-intercept form using
Slope-intercept form
Replace m with –4 and
b with –16.
Answer: The equation is
The answer is D.
Write an Equation Given Two Points
Multiple-Choice Test Item
The table of ordered pairs shows
the coordinates of two points on the
graph of a function. Which equation
describes the function?
A
B
C
D
Answer: B
x
y
–1
3
2
6
Writing Equations in Slope-Intercept Form
You may need to rewrite the
information as two points then find
the slope and y-intercept.
Write an Equation to Solve a Problem
Economy In 2000, the cost of many items increased
because of the increase in the cost of petroleum. In
Chicago, a gallon of self-serve regular gasoline cost
$1.76 in May and $2.13 in June. Write a linear equation
to predict the cost of gasoline in any month in 2000,
using 1 to represent January.
Explore You know the cost of regular gasoline in May and
June.
Plan
Let x represent the month and y represent the
cost of gasoline that month. Write an equation
of the line that passes through (5, 1.76) and
(6, 2.13).
Write an Equation to Solve a Problem
Solve
Find the slope.
Slope formula
Let
and
Simplify.
.
Write an Equation to Solve a Problem
Choose (5, 1.76) and find the y-intercept
of the line.
Slope-intercept
form
Replace m with
0.37, x with 5,
and y with 1.76.
Multiply.
Subtract 1.85
from each side.
Simplify.
Write an Equation to Solve a Problem
Write the slope-intercept form using
and
Slope-intercept form
Replace m with 0.37
and b with –0.09.
Answer: The equation is
Write an Equation to Solve a Problem
Examine
Check your result by substituting the
coordinates of the point not chosen, (6, 2.13),
into the equation.
Original equation
Replace y with
2.13 and x with 6.
Multiply.
Simplify.
Write an Equation to Solve a Problem
The average cost of a college textbook in 1997 was
$57.65. In 2000, the average cost was $68.15. Write a
linear equation to estimate the average cost of a
textbook in any given year since 1997. Let x represent
years since 1997.
Answer:
Writing Equations in Slope-Intercept Form
Writing Equations in Slope-Intercept Form
Linear extrapolation is when you use a
linear equation to predict values that are
beyond the range of the data.
Be cautious when making a prediction
using just two given points.
The model may be approximately correct
but still give inaccurate predictions.
Linear Extrapolation
Economy The Yellow Cab Company budgeted $7000
for the July gasoline supply. On average, they use
3000 gallons of gasoline per month. Use the prediction
equation
where x represents the
month and y represents the cost of one gallon of
gasoline, to determine if they will have to add to their
budget. Explain.
Original equation
Replace x with 7.
Simplify.
Answer: If gas increases at the same rate, a gallon of
gasoline will cost $2.50 in July. 3000 gallons at this price is
$7500, so they will have to add $500 to their budget.
Linear Extrapolation
A student is starting college in 2004 and has saved
$400 to use for textbooks. Use the prediction equation
where x is the years since 1997 and
y is the average cost of a college textbook, to
determine whether they will have enough money for
5 textbooks.
Answer: If the cost of textbooks increases at the same
rate, the average cost will be $82.15 in 2004. Five
textbooks at this price is $410.75, so he will not have
enough money.