Sophia Learning, College

Algebra, Milestone 3, WITH

ANSWERS

1

The graph of a linear function passes through the points

and .

Find the slope of this function.

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•

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 CORRECT

RATIONALE

SOPHIA LEARNING, COLLEGE

ALGEBRA, MILESTONE 3,

WITH ANSWERS

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CONCEPT

Determining Slope

2

The prices for a loaf of bread and a gallon of milk for two

supermarkets are shown below.

Since we have two points from a linear function, we can

use the slope formula to find the slope of the line.

Now that the numbers are plugged in, evaluate the

subtraction in both the numerator and the denominator.

In the numerator, the difference in coordinates is

minus , or . In the denominator, the difference in

coordinates is minus , which is the same as plus

, or . The slope of the line is .

The slope is the difference in coordinates from the two

points divided by the difference in coordinates from the

same two points. When plugging in the values it is

important to be consistent with which coordinates are

subtracted in the calculations.

A B

Bread $2.20 $2.50

Milk $3.60 $3.40

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Mary needs to buy bread and milk for her church picnic. At

Supermarket A, she would pay $44.20. At Supermarket B, she

would pay $44.70.

Which of the following system of equations represents this

situation?

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•

CORRECT

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•

RATIONALE

In general, the equation to represent the

total cost of buying bread and milk would

be the sum of the cost for bread and cost

for milk. To find the cost of bread and

milk, first define variables to represent the

amount of bread and milk.

Here, will represent bread, and will

represent milk. Both and will be

multiplied by their respective prices.

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CONCEPT

Writing a System of Linear Equations

3

Select the correct slope and y-intercept for the following linear

equation:

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CORRECT

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At Store A, a loaf of bread costs $2.20,

and a gallon of milk costs $3.60. We also

know that the total cost at Store A is

$44.20. So the total cost at Store A would

be expressed with this equation. We can

construct a similar equation for Store B.

At Store B, bread cost $2.50 per loaf, and

milk costs $3.40 per gallon. We also know

that the total cost at Store B is $44.70.

The total cost at Store B would be

expressed with this equation.

This is the system of equations to

represent the costs of bread and milk at

Store A and B.

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