Final Review

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

Write an equation to represent the cost of playing putt-putt at two locations: $2.00 for rentals plus $7.50 per game and $8.00 for rentals plus $6.00 per game.

Back

2 + 7.50x = 8 + 6x

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

Write the equation for the cost C after h hours of service if a plumber charges $25 for a service call plus $50 per hour.

Back

C = 25 + 50h

Front

How do you solve the equation -7x - 36 = 20 - 3x?

Back

Combine like terms to isolate x: -4x = 56, so x = -14.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

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

Back

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

Front

How do you determine if a relation is a function using a graph?

Back

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

Front

What is the first step in solving a system of equations?

Back

The first step is to express one variable in terms of the other, or to use substitution or elimination methods.