y=mx+b

Front

What does the equation y=mx+b represent in a linear function?

Back

In the equation y=mx+b, 'm' represents the slope of the line, 'b' represents the y-intercept, and 'x' is the independent variable.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

How do you determine the slope in a real-world scenario?

Back

The slope represents the rate of change; it can be determined by the ratio of the change in the dependent variable (y) to the change in the independent variable (x).

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0; it represents the starting point of the function on the y-axis.

Tags

CCSS.HSF-IF.C.7A

Front

How can you model a situation with a fixed cost and a variable cost using a linear equation?

Back

You can model it using the equation y=mx+b, where 'b' is the fixed cost and 'm' is the variable cost per unit.

Tags

CCSS.HSF.LE.B.5

Front

In the context of a taxi service, how would you express the total charge as a function of miles driven?

Back

The total charge can be expressed as y=2x+5, where 'x' is the number of miles driven, $2 is the cost per mile, and $5 is the pickup fee.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

If a plumber charges a service fee plus an hourly rate, how would you write this as a linear equation?

Back

You would write it as y=15x+40, where 'x' is the number of hours worked, $15 is the hourly rate, and $40 is the service fee.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you calculate the total cost for a service that has both a fixed fee and a variable fee?

Back

You add the fixed fee to the product of the variable fee per unit and the number of units used.

Tags

CCSS.HSF.LE.B.5

Front

What is the formula to calculate the depreciation of an asset over time?

Back

The formula is y = initial value - (depreciation rate * number of years), where 'y' is the value after depreciation.

Front

How would you express the cost of a pizza with a base price and additional toppings?

Back

You would express it as y=0.50x+8, where 'x' is the number of additional toppings, $0.50 is the cost per topping, and $8 is the base price.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean if a function is linear?

Back

A linear function means that the relationship between the independent and dependent variables can be represented by a straight line on a graph.

Tags

CCSS.8.F.A.3