Slope Intercept

Slope Intercept

In order to write an equation in Slope Intercept Form, you need 2 things:

1. A slope (m)
2. A y-intercept (b)

 $y=mx+b$  

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

It's easy when we are given the slope and the y-intercept....

But, what about when we have a piece missing?

Write an equation of the line in Slope Intercept Form that goes through the point (-3,7) and has a slope of 1/3

• Use our handy dandy formula: $y=mx+b$   

• Know that -3 is x and 7 is y

• Know that 1/3 is m

• Substitute those values into  $y=mx+b$  

• 7=(1/3)(-3) + b

• Solve for b

So now we have a slope (1/3) and a y intercept (8).
Guess what? We now have everything we need to write a Slope Intercept equation:

 $y=\ \frac{1}{3}x+8$  

Now let's go one step further... We are just given 2 points and that's it.... uh oh $\left(3,-1\right)\ \left(4,7\right)$  

• Use the slope formula to find the slope 

• Once you have the slope, choose one of your 2 points (it doesn't matter which you choose - I kind of like to stick with the one on the left)

• Go through the exact same steps we just did in the previous slides

Multiple Choice

What is the formula for finding slope?

• $y=mx+b$

• $Ax+By=C$

• $\frac{y_2-y_1}{x_2-x_1}$

So now we have our slope: $8$   and we now need to find our y intercept.  Let's choose the point (3,-1).  

Now we just follow the exact same steps as the previous example.

* Substitute the values for x and y and m into the slope intercept formula (you will answer this on the next slide, so write it down!)

Multiple Choice

After substituting in the values, what does the equation look like?

• $-1=8\left(3\right)+b$

• $3=8\left(-1\right)+b$

Open Ended

Now we can write our Slope Intercept Equation :)

We have a slope of 8 and a y intercept of 25.

What is the equation of the line?