Graphs of Linear Functions

Presentation

•

Mathematics

•

8th Grade

•

Hard

•

CCSS

8.F.A.3, 8.EE.B.5, HSA.REI.D.10

Standards-aligned

Sarah Parnell

Used 179+ times

FREE Resource

7 Slides • 20 Questions

Graphs of Linear Functions

Slope Intercept Form Equation

y = mx + b
m is the slope (rate of change; rise/run)
b is the y-intercept (starting value)

Multiple Choice

Identify the slope as positive, negative, zero or undefined.

positive

negative

zero

undefined

Multiple Choice

What is the y-intercept of this line: y = 2/3x - 4

2/3x

-4

Multiple Choice

What is the slope of this line: y = 6x + 4

1/6

Graphing using slope intercept form

Plot the y-intercept on the y-axis
Determine the slope
Use the slope to move up (if the slope is positive) or down (if the slope is negative) from the point on the y-axis then to the right.

Multiple Choice

What is the y-intercept of this graph?

(0,1)

(0,-2)

(0,0)

(0,3)

Multiple Choice

Find the slope and y - intercept

y = 1/2x - 1

slope: 1/2 y-intercept: -1

slope: 2 y-intercept: -1

slope: 1/2x y-intercept: 1

slope: 2 y-intercept: 5

Multiple Choice

When you graph a line using slope-intercept form (y=mx+b), you graph the ___________ first and then use the ___________ to find the second point.

origin; slope

slope; y-intercept

y-intercept; x-intercept

y-intercept; slope

Multiple Choice

Which is the graph of y= -x + 2?

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

Write the equation for the line in slope-intercept form.

y= -1x+3

y= 4x+3

y=1/4x+3

y= -4x+3

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

Multiple Choice

Write the equation of the line.

y= -1x-3

y= -3x-1

y=-1/3x-1

y= -3x-3

Writing equations from key information

Always start with y = mx + b
If you know the slope and y-intercept, plug in for m and b
If you only know the slope and a point, plug in the slope and the x and y values to solve for b

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

y=3/2x+3

y=2/3-3

y=2/3x-3

y=2/3x+3

Multiple Choice

What is the equation of the line that has a slope of 5 and goes through the point (2,7)?

y = 5x + 3

y = 1/5x - 3

y = 1/5x + 3

y = 5x - 3

Multiple Choice

What is the equation of the line passing through points (1,1) and (3,-5).

y = -3x + 4

y = 3x - 4

y = -3x - 4

y = 3x + 4

Converting to slope-intercept form

Step 1: distribute if you see parentheses
Step 2: combine like terms
Step 3: isolate y
Step 4: write in the form y=mx+b

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = -2(x + 4)

y=2x-5

y=-2x+7

y=-2x-5

y=-2x +1

Multiple Choice

What is the first step to convert this equation into slope-intercept form?
$y+4=-9\left(x+3\right)$

Subtract 4 from both sides of the equation

Add 4 to both sides of the equation

Distribute -9 to everything in the parentheses

Distribute 9 to everything in the parentheses

Multiple Choice

Which equation represents 4x - 2y = 6 in slope intercept form.

y = 2x - 3

y = -2x + 3

y\ =\ \frac{1}{2}x\ -\ 3

y = 2x + 8

Linear vs. Non-linear

Linear functions form a straight line and have a constant increase or decrease of y as x increases or decreases
Non-linear functions do not form a straight line and as x increases, y does not increase at a constant rate

Multiple Choice

$y\ =\ 6x\ +\ 5$

Linear

Nonlinear

Multiple Choice

Linear or Nonlinear?

Linear

Non-Linear

Multiple Choice

Linear or Nonlinear?

Linear

Non-Linear

Multiple Choice

Linear or Nonlinear?

Linear

Non-Linear

Graphs of Linear Functions

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