Unit 3 Lesson 1

Understand Linear and Nonlinear Functions

xy-plane

• x-axis (horizontally left-to-right)

• y-axis (vertically down-to-up)

• positive values x-right / y-up

• negative values x-left / y-down

Slope Intercept Form

• Follows the format y=mx+b

• Each letter tells us an important feature of the function.

• m is the slope of the line

• b is the y intercept (where the line crosses the y axis)

Multiple Choice

What is the slope of the line

$$y=-\frac{1}{2}x-4$$  

• $$-\frac{1}{2}$$  

• -4

• y

• x

​slope

(m)

• steepness of a line

• ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Positive and Negative Slope

• If a line has a positive slope, it points up to the right side of the graph

• If a line has a negative slope, it points up to the left side of the graph
  

Multiple Choice

Does the following graph have a positive slope or a negative slope?

• Positive

• Negative

• Neither

​

Find the slope of the line

​Two ways

1) difference of y's over differences of x's

2) COUNT!
-start at one point, count down/up and then over

​y-intercept

(b)

• ​Where the line crosses the y-axis

• At this point, x=0

• To find the y-intercept (b), set x as zero in the equation.

• (0, b)

Multiple Choice

What is the y intercept of this equation?

$$y=-3x-7$$  

• -3

• -7

• y

• x

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Multiple Choice

What is the y-intercept?

• (2,0)

• (0,2)

• (0,-2)

• (-2,0)

​Slope-Intercept Form

Multiple Choice

Write an equation in slope-intercept form:

$$Slope\ \left(m\right)\ =\ 10$$  

$$y-intercept\ \left(b\right)\ =\ \left(0,\ 8\right)$$  

• $$y\ =\ 8x\ -\ 10$$  

• $$y\ =\ 8x\ +\ 10$$  

• $$y\ =\ 10x\ -\ 8$$  

• $$y\ =\ 10x\ +\ 8$$  

Multiple Choice

Write an equation in slope-intercept form:

$$Slope\ \left(m\right)=\ \frac{3}{8}$$  

$$y-intercept\ \left(b\right)\ =\ \left(0,\ -1\right)$$  

• $$y\ =\ \frac{3}{8}x\ -\ 1$$  

• $$y\ =\ \frac{3}{8}x\ +\ 1$$  

• $$y\ =\ 1x\ +\ \frac{3}{8}$$  

• $$y\ =\ 1x\ -\ \frac{3}{8}$$  

From a Graph

Find the Slope

Find the y-intercept

Plug in the values to y = mx + b

Drag and Drop

Write the equation of the line.

y=​ ​

Placeholder

x​

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

-5/4

-

1

+

5

4

5/4

4/5

-4/5

-1

Multiple Choice

Write the equation of the line.

• $$y=\frac{3}{5}x+1$$

• $$y=\frac{3}{5}x-1$$

• $$y=\frac{5}{3}x+1$$

• $$y=\frac{3}{5}x+1$$

Graphing Linear Functions

• Only need two points

• 1st point: start at the y-int (b)

• 2nd point: use slope to find it!

Multiple Choice

 Select the graph for $$y=2x+3$$  

Multiple Choice

 Select the graph for $$y=-\frac{4}{3}x-1$$  

​Graphing an Equation

​To graph an equation, it is easiest to make a function table first.


1) select values for x
2) plug them into the equation
3) solve for y.
4) this gives us a coordinate pair (x, y)
5) plot the points on a coordinate plane

​

​

​

Using Tables to Determine Linear and Nonlinear Relationships

to determine if a slope is constant, compare the slope between several ordered pairs

- if the slope is constant, the function is linear

- if the slope is not constant, the function is nonlinear

Multiple Choice

The table represents a function. Is it linear or non-linear?

• Linear

• Nonlinear

Multiple Choice

Is the table linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

The slope of the line shown on the table is

• $$-\frac{3}{4}$$  

• $$\frac{3}{4}$$  

• $$-\frac{1}{3}$$  

• $$\frac{3}{10}$$  

Multiple Choice

The slope of the line shown on the table is

• $$\frac{2}{5}$$  

• $$-\frac{2}{5}$$  

• $$\frac{5}{2}$$  

• $$-\frac{5}{2}$$  

Multiple Choice

Is this function linear or non-Linear?

• Linear

• Non-Linear

Multiple Choice

Is this function linear or non-Linear?

• Linear

• Non-Linear

From a Graph

• When graphed, a linear function forms a single straight line.

• When graphed, a nonlinear function does not form a single straight line.

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

Determine if the graph is linear or nonlinear.

• Linear

• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear

• Nonlinear

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