Linear Functions (8.5G; 8.5I)

The table shows y as a function of x. Which ordered pairs can also belong to the function?

Select TWO correct answers.

• (-4, 3)

• (-2, 3)

• (4, 3)

• (6, 8)

• (9, 8)

Answer explanation

To maintain a relation as a function, each input (or x-value) must map to exactly one output (or y-value). In other words, no two ordered pairs can have the same x-value with different y-values.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

The graph of a linear function passes through the points (-2, 70) and (6, -50).

Which equation represents the function?

• y = -3/2x + 40

• y = -3/2x + 4

• y = -15x + 4

• y = -15x + 40

Answer explanation

Step 1: Find the slope

To find the slope, subtract the y-value of the second point from the y-value of the first point. Then, subtract the x-value of the second point from the x-value of the first point. Finally, divide the difference in y-values by the difference in x-values. This gives the slope.

For example, with the points (-2, 70) and (6, -50), subtract 70 from -50 to get -120, and subtract -2 from 6 to get 8. Dividing -120 by 8 gives a slope of -15.

Step 2: Use the slope in the equation

Now that you know the slope, write the equation in the form "y equals the slope times x plus some number," which is called the y-intercept. In this case, the equation will be something like: "y equals -15 times x plus something."

Step 3: Find the y-intercept

To find the y-intercept, pick one of the two points and use it to solve for the missing number (the y-intercept). Take the point (-2, 70) as an example. You know that when x is -2, y is 70. Substitute those values into the equation. Multiply the slope, -15, by -2 (the x-value), which gives 30. Then figure out what number you would need to add to 30 to get 70. The missing number is 40, which is the y-intercept.

Step 4: Write the final equation

Now you know the slope is -15 and the y-intercept is 40. So, the equation of the line is: "y equals -15 times x plus 40."

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

The graph of a linear function is shown on the grid.

Determine the equation of the line represented by the graph.

• y = 3/2x - 4

• y = 3x - 6

• y = 3/2x + 6

• y = -3/2x - 4

Answer explanation

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which graph represents y as a function of x?

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Answer explanation

To determine whether a graph represents a function, you can use the Vertical Line Test.

1. Visualize a vertical line (a straight line parallel to the y-axis) moving across the graph.

2. Check how many times the vertical line intersects the graph at any given point.

Interpretation:

• If any vertical line touches the graph at more than one point, the graph does not represent a function.

• If every vertical line touches the graph at exactly one point, the graph does represent a function.

Which equation can be used to describe the relationship between x and y shown in the graph?

• y = 3x + 2

• y = -3x - 6

• y = 3x -6

• y = -3x + 2

Answer explanation

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which graph represents y as a function of x?

• 
• 
• 
• 

Answer explanation

To determine whether a graph represents a function, you can use the Vertical Line Test.

1. Visualize a vertical line (a straight line parallel to the y-axis) moving across the graph.

2. Check how many times the vertical line intersects the graph at any given point.

Interpretation:

• If any vertical line touches the graph at more than one point, the graph does not represent a function.

• If every vertical line touches the graph at exactly one point, the graph does represent a function.

Frankie bought a new computer. He made an initial payment of $50 to the store, and he will pay $30 each month until the computer is paid off. Which equation represents the relationship between m, the number of monthly payments Frankie has made, and t, the total amount that Frankie has paid to the store?

• t = 50m + 30

• t = 30m - 50

• t = 50m - 30

• t = 30m + 50

Answer explanation

1. Initial Payment: Frankie makes an initial payment of $50.

2. Monthly Payments: Frankie then pays $30 for each month he continues to make payments.

1. Total Amount After Monthly Payments: The total amount paid from monthly payments after m months is 30m.

2. Adding the Initial Payment: To find the total amount paid, you need to add the initial payment to the total from the monthly payments.

Equation

So, the equation that represents the relationship is:

t=50+30m

Tags

CCSS.HSF-BF.A.1A

Which graph represents y as a function of x?

• 
• 
• 
• 

Answer explanation

To maintain a relation as a function, each input (or x-value) must map to exactly one output (or y-value). In other words, no two ordered pairs can have the same x-value with different y-values.

Tags

CCSS.8.F.A.1

Mr. Leonard is renting a car for one day. The table shows the total amount he will be charged for the car based on the number of miles.

Which equation best represents c, the number of dollars Mr. Leonard should be charged for driving m miles?

• c = 0.10m + 30

• c = 30m + 0.10

• c = 0.50m + 30

• c = 30m + 0.50

Answer explanation

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which graph represents y as a function of x?

• 
• 
• 
• 

Answer explanation

To maintain a relation as a function, each input (or x-value) must map to exactly one output (or y-value). In other words, no two ordered pairs can have the same x-value with different y-values.