Unit 4- Linear Equations

Slope-intercept

Slope is also known as

• the Constant Rate of Change

•  $\frac{Rise}{Run}$  

• m

The Constant Rate of change

• A rate of change is a rate that describes how one quantity changes in relation to another.

• A constant rate of change is the rate of change of a linear relationship. For example, the rate of change on a graph.

• It is shown as

   $\frac{\Delta y}{\Delta x}$  which is the  $\frac{\left(change\ of\ y\right)}{\left(change\ of\ x\right)}$  

When solving CROC from a table we have to find the rate of change on both sides. For instance, the change of y from 100 to 150 is a positive change of 50. The change of x from 10 to 15 is a positive change of 5. So when I put it into $\frac{change\ of\ y}{Change\ of\ x}$  form it should look like this:  $\frac{50}{5}$  . When I simplify this my answer would be 10. My CROC is 10. My slope is 10. 

Poll

Slope is also known as....(choose all that apply)

• Constant Rate of Change

• Constant of Proportionality

• m

•  $\frac{rise}{run}$  

Solve CROC on a table:

 $\frac{\left(change\ of\ y\right)}{\left(change\ of\ x\right)}$  

Write your answer down and have it handy

Fill in the Blanks

Tell me the answer to the CROC on the previous slide.

Just the number.

Poll

How many of you prefer this type of quiz or lesson?

• Yes

• No

When solving CROC on a graph, we are going to make a T-chart using the coordinate points on the graph. Using that same sheet of paper, make a T-chart and write down the coordinates from this example.

This is what my T-chart looks like. Yours should look similar to this. Now that this is done, solve the CROC and have your answer handy. :)

Fill in the Blanks

What was the CROC from the previous slide.

Remember that when we are solving for slope on a graph with numbers we MUST PAY ATTENTION TO THE NUMBER CHANGE! Notice how I took the coordinates and made a T-chart. The first coordinate of (1,40) LOOKS like a rise of 1 and a run of 1. Instead it is a rise of 40 and a run of 1. That makes my slope=40 and not 1.

On a sheet of paper, solve for CROC which is also our SLOPE! Keep it handy :)

Fill in the Blanks

What was the CROC (slope) of the graph on the previous slide?

Remember that when we are solving for CROC, we are also solving for m, which is SLOPE.
On a graph, it's beneficial for us to use $\frac{Rise}{Run}$  to solve for our Slope/CROC. 

On this example, we had a positive rise of 2, and a positive run of 3. Since we put rise over run, the slope is  $\frac{2}{3}$  

On the same sheet of paper, find the slope, $\frac{rise}{run}$ , of this graph using the points on the graph. Keep your answer handy. 

Multiple Choice

What is the slope of the graphed line on the previous slide? Remember to simplify if needed.

• 2

• 1/2

• -2

• -1/2

Finding y-intercept

• The y-intercept is the point where the line intersects with the y-axis.

• The y-intercept is represented by the letter b.

• As a football player, you have a quarterback that throws the ball to the receiver. If a player from the other team gets the ball it is call an interception. Think of the other player as the y-axis. The point where he received the ball instead is the y-intercept. I know you guys call that a pick.

• The same is true for basketball players. When a teammate passes the ball to you and someone jumps in and steals the ball, it's another type of interception.

Finding the y-intercept on a table

Any time you are looking for the y-intercept, x must be zero. On a graph, it can only intercept the y-axis if x is zero. So, on a table, we are looking for the ordered pair (x,y) to have a 0 for x.

On this table the spot where x=0 is the very first ordered pair of (0,120). That means that 120 is our y-intercept. So it would look like this: b=120.

Finding y-intercept on a graph

means we want to find the point where our line intersects the y-axis. The y-axis is the vertical line highlighted in blue. The arrow is pointing to the spot where our line intersects the y-axis. That spot is labeled with the coordinates. Notice that, again, x is zero. That means the y in the ordered pair is our y-intercept (b). In the first one b=-1, in the second one b= 1.

Let's try finding the y-intercept on a table. Keep your answer handy!

Fill in the Blanks

The y-intercept on the previous slide is

Let's try finding the y-intercept using the points given on the graph. Keep your answer handy!

Fill in the Blanks

What was the y-intercept of the graph on the previous slide?

Slope-intercept from Graphs

• The equation of a line is written in slope-intercept form which is y=mx+b

• Each equation must have a slope (m) and a y-intercept (b).

• Here, the y-intercept (b)=-4 and the slope(m)=1/1 which is 1. When we put all the information together, we have y=1x-4

Slope-intercept from a table

• y-intercept on a table is when we look for x=0. The corresponding y will be our y-intercept (b). Here, it is b=6

• When finding slope(m) we find the CROC. The   $\Delta y$ from 12 to 6 is -6. The  $\Delta x$ from -2 to 0 is +2. Our CROC is  $-\frac{6}{2}$  simplified to m=-3.

• In slope-intercept form: y=-3x+6

Let's create an equation! Take the information from this table and place it in slope-intercept form (y=mx+b). Don't forget....you need the y-intercept, and the slope...Keep your answer handy!

Fill in the Blanks

What is the equation of the line in the previous slide? Remember to put it into slope-intercept form (y=mx+b). When you put your answer in include all the required information

for example... y= 3x+8... Now put in your answer.

Let's create an equation! Take the information from this graph and place it in slope-intercept form (y=mx+b). Don't forget....you need the y-intercept, and the slope...Keep your answer handy!

Fill in the Blanks

Write the equation of the line in the previous slide. Remember to put the answer in slope-intercept form (y=mx+b).