Equations as Functions

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of y in a linear equation when given x?

Back

To find the value of y in a linear equation, substitute the given value of x into the equation and solve for y.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What is the difference between a function and a non-function?

Back

A function is a relation where each input (x) has exactly one output (y). A non-function may have an input that corresponds to multiple outputs.

Front

How can you determine if a mapping is a function?

Back

You can determine if a mapping is a function by checking if any x-value is paired with more than one y-value. If it is, then it is not a function.

Front

What is the output of the function y = 4x + 5 when x = 4?

Back

The output is 21, calculated by substituting x = 4 into the equation: y = 4(4) + 5 = 16 + 5 = 21.

Front

What is the output of the function y = x + 3 when x = -2?

Back

The output is 1, calculated by substituting x = -2 into the equation: y = -2 + 3 = 1.

Front

What is the output of the function y = 5 - 6x when x = -5?

Back

The output is 35, calculated by substituting x = -5 into the equation: y = 5 - 6(-5) = 5 + 30 = 35.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.