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

Find the y-intercept. Just type the number

Fill in the Blanks

Find the y-intercept. Just type the number

Fill in the Blanks

Determine the y-intercept from the following points: (-2, 3), (0, 5), (2, 7).

Just type the number

Fill in the Blanks

Determine the y-intercept from the following points: (0, -2), (1, 5), (2, 12).

Just type the number

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

Write an equation for this graph.

Type your answer with no spaces.

Fill in the Blanks

Write an equation for this graph. Notice that the axes are counting by twos.

Type your answer with no spaces.

Fill in the Blanks

Write an equation using the table.

Type your answer with no spaces.

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

Write an equation for this line.

Multiple Choice

• 
  

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

• $$-\frac{1}{4}$$

• $$-4$$

• $$4$$

Multiple Choice

• $$0$$

• $$-3$$

• $$undefined$$

• $$-1$$

Fill in the Blanks

Write an equation for the line.

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.