Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, defined by the equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Write the equation for the cost of snowboarding if the resort charges $15 per hour and $25 for board rental.

Back

y = 15x + 25, where y is the total cost and x is the number of hours.

Front

What is the definition of a function?

Back

A function is a relation where every input (x) has exactly one output (y).

Front

How do you find the output of a function given an input?

Back

Substitute the input value into the function's equation and solve for the output.

Front

Given the function f(x) = 6x - 5, find f(-3).

Back

f(-3) = 6(-3) - 5 = -18 - 5 = -23.

Front

What is the equation for the price of an ice cream with a base price of $3.95 and $0.85 for each topping?

Back

p = 0.85t + 3.95, where p is the total price and t is the number of toppings.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphed as a straight line, which means it has a constant rate of change.

Front

How can you determine if a relation is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.