What is a linear function?

A linear function is a function that, when graphed, forms a straight line.

What makes a function linear?

• Linear functions have two variables

• x = independent variable, such as year or time

• y = dependent variable, such as dollars earned or miles traveled

• As previously mentioned, their graphs will form a straight line

Linear Equations

Standard form, slope-intercept form, and point-slope form.

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

The line passes the vertical line test (gray line that is labeled pass). This graph is a linear function. The domain are the x values and the range are the y values.

D: All real numbers or (-∞, ∞)

R: All real numbers or (-∞, ∞)

​Domain and Range of a Linear Function.

​AKA Maxima and Minima!

x and y intercepts

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Writing Equations from graphs

• Identify the y-intercept (where the line crosses the y-axis)

• Determine the slope (rise/run - how you have to move to get from one point on the line to another)

• Plug in the slope for m, the y-intercept for b in y=mx+b

​You can also use DESMOS