Page 140 - Math Course 3 (Book 1)

Equations with Slope and Points on the Line

MO. 4 - L4b Check
Check your result by substituting the coordinates of
Equations Using Two Points the point not chosen, (7, 2.82), into the equation.

on the Line y = 0.22x + 1.28 Original equation
?
2.82 = 0.22(7) + 1.28 Replace y with 223 and
x with 24.
Let’s Begin 2.82 = 1.54 + 1.28 Multiply.
?

2.82 = 2.82
Real World Example

ECONOMY ECONOMY

In 2005, Tim’s cost for self-serve regular On average, Tim uses 25 gallons of
gasoline was $2.60 on the first of June gasoline per month. He budgeted $80
and $2.82 on the first of July. Write a linear for gasoline in October. Use the prediction equation
equation to predict Tim’s cost of gasoline the first in Example 3 to determine if Tim will have to add to
of any month in 2005, using 1 to represent January.
his budget. Explain.
Explore y = 0.22x + 1.28 Original equation
You know the cost in June is $2.60. You know the
cost in July is $2.82. y = 0.22(10) + 1.28 Replace x with 10.

Plan y = 3.48 Simplify.
Let x represent the month. Let y represent the cost.
Write an equation of the line that passes through
(6, 2.60) and (7, 2.82). If gasoline prices increase at
the same rate, a gallon will cost
Solve Find the slope. Answer $3.48 in October. 25 gallons at
this price is $87, so Tim will have
y – y Slope formula to add at least $7 to his budget.
2
m = x – x 1
2 1
2.82 – 2.60 Let (x , y ) = (6, 2.60)
1
1
m = and (x , y ) = (7, 2.82). Your Turn!
7 – 6 2 2
m = 0.22 Simplify.
Real World Example
Choose (6, 2.60) and find the y-intercept of the line. The average cost of a college textbook in 1997
was $57.65. In 2000, the average cost was $68.15.
y = mx + b Slope-intercept form Write a linear equation to estimate the average
cost of a textbook in any given year since 1997.
2.60 = 0.22(6) + b Replace m with 0.22, x with Let x represent years since 1997.
6, and y with 2.60.
A. y = 3.5x + 57.65
1.28 = b Simplify. B. y = 3.5x + 68.15
C. y = 57.65x + 68.15
Write the slope-intercept form using m = 0.22, and D. y = –3.5x – 10
b = 1.28.
Answer
y = mx + b Slope-intercept form

y = 0.22x + 1.28 Replace m with 0.22 and b
with 1.28.
Therefore, the equation is
Answer y = 0.22x + 1.28.

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