Chapter 3 Linear Equations - Teacher Copy

Linear Equations

We must understand slope before we can understand linear equations.

​Finding Slope

• From an equation

• From a graph

• From two points

• From a table

Slope-intercept form is written as y = mx + b,

where m is the slope.

Let's look at a few examples.

​

Finding Slope from an Equation.

​

Example 1:

Finding Slope from an Equation.

​

m =

Example 2:

m =

Example 3:

m =

To find slope from a graph we 1) choose two points on the line, and 2) count the rise and run from one point to the next.

Let's look at a few examples.

​

Finding Slope from a Graph.

Example 1:

Finding Slope from a Graph.

m =

Example 2:

m =

Example 3:

m =

To find slope from two points we 1) choose two points, 2) label the coordinates x₁, y₁ and x₂, y₂, 3) plug the values into slope formula and solve.

Let's look at a few examples.

​

Finding Slope from Two Points.

Example 1:

(2, 5) and (4, 13)

Finding Slope from Two Points.

m =

Example 2:

(-1, -3) and (2, -5)

m =

Example 3:

(3, 5) and (7, 13)

m =

Finding slope from a table is very similar to finding slope from two points. 1) Choose two points from the table, 2) label the the coordinates x₁, y₁ and x₂, y₂, 3) plug the values into slope formula and solve.

Another option is finding a pattern in the table.

Let's look at a few examples.

​

Finding Slope from a Table.

Example 1:

Finding Slope from a Table.

m =

Example 2:

m =

Example 3:

m =

Multiple Choice

Find the slope of the line.

• -2

• 2

• -1

• 1

Multiple Choice

Find the slope of the line that passes through

(10, 1) and (5, 2)

• 1/5

• -1/5

• 5

• -5

Multiple Choice

Find the slope from the table:

• -2/5

• 5/-2

• 5/2

• 2/5

​Finding y-intercept

• From an equation

• From a graph

• From a point or table

In the slope-intercept form equation, y = mx + b,

b is the y-intercept.

Let's look at a few examples.

​

Finding y-intercept

from an Equation.

​

Example 1:

Finding y-intercept

from an Equation.

​

b =

Example 2:

b =

Example 3:

b =

To find the y-intercept of a graph, we locate the point where the line crosses the y-axis.

Let's look at a few examples.

​

Finding y-intercept from a Graph.

Example 1:

Finding y-intercept from a Graph.

b =

Example 2:

b =

Example 3:

b =

To find the y-intercept from a point or table, we have to look for the value of y when x is 0.

Let's look at a few examples.

​

Finding y-intercept from a point or a table.

​(0, 9)

Multiple Choice

Find the y-intercept of the line.

• -2

• 3

• -3

• 1

Multiple Choice

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

• slope: 5

  y-intercept: (0,3)

• slope: 3/2

  y-intercept: (0,3)

• slope: 4

  y-intercept: (0,3/2)

• slope: 1/5

  y-intercept: (0,5)

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2

• 3

• 5

• Cannot be Determined

Fill in the Blanks

Fill in the Blanks

Once you find the slope and y-intercept, you can write an equation in slope intercept form.

Let's try.

​

Writing an Equation.

Example 1:

Writing an Equation.

m=

b =

y=

Example 2:

Example 3:

m=

b =

y=

m=

b =

y=

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Choice

• positive

• negative

• zero

• undefined

Multiple Choice

• positive

• negative

• zero

• undefined

Multiple Choice

• $$-\frac{1}{4}$$

• $$-4$$

• $$\frac{1}{4}$$

• $$4$$

Multiple Choice

• $$-\frac{5}{2}$$

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$-\frac{2}{5}$$

Multiple Choice

• $$0$$

• $$5$$

• $$undefined$$

• $$\frac{1}{5}$$

Fill in the Blanks

Multiple Choice

• 
  

  $$\frac{1}{4}$$
  

• $$-\frac{1}{4}$$

• $$-4$$

• $$4$$

Multiple Choice

• $$0$$

• $$-3$$

• $$undefined$$

• $$-1$$

Fill in the Blanks

Let's review all we've learned...

Multiple Choice

Write the equation of a line with  slope  $$m=\frac{1}{4}$$   and y-intercept.

$$b=3$$

• $$y=\frac{1}{4}x+3$$  

• $$y=3x+\frac{1}{4}$$  

• $$y=4x+3$$  

• $$y=-\frac{1}{4}x+3$$  

Multiple Choice

Write the equation of a line with  slope  $$m=\frac{2}{3}$$   and y-intercept.

$$b=1$$

• $$y=x+\frac{2}{3}$$  

• $$y=\frac{2}{3}x+1$$  

• $$y=\frac{1}{3}x+2$$  

• $$y=-\frac{2}{3}x+1$$  

Multiple Choice

Write the equation of a line with  slope  $$m=-\frac{1}{3}$$   and y-intercept:

$$\left(0,-4\right)$$

• $$y=\frac{1}{3}x+4$$  

• $$y=4x+\frac{1}{3}$$  

• $$y=-\frac{1}{3}x-4$$  

• $$y=-3x-4$$  

Multiple Choice

Write the equation of the line graphed below.

• $$y=\frac{3}{2}x+2$$

• $$y=3x+2$$

• $$y=-\frac{3}{2}x+2$$

Multiple Choice

Write the equation of the line graphed below.

• $$y=-x+2$$

• $$y=x-1$$

• $$y=-2x+1$$

Poll

How do you feel about today's activity?

• 1. I am still lost.

• 2. I can do it with some help.

• 3. I can do it myself.

• 4. I could teach someone else.