Unit 4: Slope and Y-Interecept

Standard

Slope Intercept Form:      y = mx + b

The variable m is the slope, it explains the steepness of a line of how slanted the line is.

The variable b is the y-intercept, this is where the line crosses or intersects the y-axis.

https://www.desmos.com/calculator

http://www.shmoop.com/video/slope-intercept-form/

Slope: m

Slope is how steep a straight line is.
When finding the slope from a line on a graph we use the method of rise over run .
  • Rise is how far up
  • Run is how far along

rise over runn

You can also think of it as the change in y over the change in x.
gradient
EXAMPLE #1:
rise over run
The slope here is 4/6 which can simplify to 2/3.
EXAMPLE #2:
Slope
In this example the slope is 3/5.

For more information on slope click here.

Practice Problems

Get your SLOPE on!

TEST YOUR SELF ON LINES HERE!!!!

https://my.hrw.com/wwtb/api/viewer.pl

Here is a video of slope as a rate of change.

Y Intercept: b

Y intercept is where a straight line crosses the Y axis of a graph.

Example:

Y intercept

In the above diagram the line crosses the Y axis at 1.

So the Y intercept is equal to 1.

For more information on intercepts click here.

Practice Problems

Get your Y-intercept on!

Slope Intercept Form

y = mx + b

m = Slope (how steep the line is)

b = the Y Intercept (where the line crosses the Y axis)\

y=mx+b graph

How do you find “m” and “b”?

  • b is easy: just see where the line crosses the Y axis.
  • m (the Slope) needs some calculation. Remember to write slope as a fraction.

Example 1)

y=2x+1 graph

The fastest and easiest thing to find first when looking at a graph is the y-intercept (b).

Here we see that the line crosses the y-axis at positive 1.

So, b = 1 .

 Now to find the slope (m) we will use rise over run:

  • Rise is how far up
  • Run is how far along

In this example the rise is 2 and the run is 1.

So, m = 2/1 .

Now that I know m = 2/1 and b = 1 I can plug them into the equation for slope intercept form y = mx + b.

y = (2/1) x + 1

^^^^^ This is the equation of the line.
For  more information on y = mx + b click here.

 Practice Problems

Get your Slope Intercept on!

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