Algebra, Milestone 3, WITH ANSWERS
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.
•
•
•
•
CORRECT
RATIONALE
,Algebra, Milestone 3, WITH ANSWERS
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
,Algebra, Milestone 3, WITH ANSWERS
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?
•
•
CORRECT
•
•
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.
, Algebra, Milestone 3, WITH ANSWERS
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:
•
CORRECT
•
•
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.
•
•
•
•
CORRECT
RATIONALE
,Algebra, Milestone 3, WITH ANSWERS
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
,Algebra, Milestone 3, WITH ANSWERS
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?
•
•
CORRECT
•
•
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.
, Algebra, Milestone 3, WITH ANSWERS
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:
•
CORRECT
•
•
