Graphing Linear Functions

Graphing Linear Functions

Integrated Math III

​Period 2 and 4

What is a linear function?

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

Multiple Choice

Which of these is a graph of a linear function?

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:

Fill in the Blanks

What is the slope of a line between (-4,14) and (-16,8)? Reminder! 

Formula:

$m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$  

Multiple Choice

Calculate the slope of a line that passes through these points. (1,3)(-1,7)

• -2

• 2

• -5

• -1/2

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!

Multiple Choice

The domain of a linear function is...

• all real numbers

• $$\left(-\infty,\ \infty\right)$$

• $$\left\{x\ \ l\ \ x\in R\right\}$$

• all of the above

Multiple Choice

the set of all possible y-values

• Domain

• Range

• Interval Notation

• Inequality Notation

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

Multiple Choice

Which equation matches the graph? (Click me to see the image)

• y = 2x

• y = 1/4 x + 2

• y = 1x + 4

• y = -2x

​You can also use DESMOS

Poll

I can graph Linear Equations using a variety of methods.

  RED - Not there at all

YELLOW - Not there yet but will be with practice

GREEN - I am good to go!