Unit 1 Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 (positive or negative).

Front

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis. To find it, set y = 0 and solve for x.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined rate of change.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning it does not rise or fall as it moves along the x-axis.

Front

How can you determine if a linear equation is in slope-intercept form?

Back

A linear equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept is the value of y when x = 0. It represents the starting point of the line on the y-axis.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the x- and y-intercepts, plot these points on a coordinate plane, and draw a straight line through them.