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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 CORRECT

RATIONALE

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Since we have two points from a linear function,

we can use the slope formula to find the slope of

the line.

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.

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 .

CONCEPT

Determining Slope

2

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

for two supermarkets are shown below.

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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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.

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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