Graphing Linear Equations and 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

What does the slope of a line represent?

Back

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

Front

What is the y-intercept?

Back

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

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means they intersect at a right angle.

Front

What is the equation of a line that is horizontal?

Back

The equation of a horizontal line is of the form y = b, where b is a constant.

Front

What is the equation of a line that is vertical?

Back

The equation of a vertical line is of the form x = a, where a is a constant.

Front

How can you determine if a point lies on a line?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation of the line and see if the resulting y-value matches the y-value of the point.

Front

What is a function?

Back

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

Front

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

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.