Use the formula y=mx+ c to work out the value ofy when m=8 x=3 c=4

m =  21 = 2

b = 1 (value of y when x=0)

So: y = 2x + 1

With that equation you can now ...

... choose any value for x and find the matching value for y

For example, when x is 1:

y = 2×1 + 1 = 3

Check for yourself that x=1 and y=3 is actually on the line.

Or we could choose another value for x, such as 7:

y = 2×7 + 1 = 15

And so when x=7 you will have y=15

Positive or Negative Slope?

Going from left-to-right, the cyclist has to Push on a Positive Slope:

negative slope   zero slope   positive slope

Example 2

y=-3x graph

m =  −31 = −3

b = 0

This gives us y = −3x + 0

We do not need the zero!

So: y = −3x

Example 3: Vertical Line

graph x=2

What is the equation for a vertical line?

The slope is undefined ... and where does it cross the Y-Axis?

In fact, this is a special case, and you use a different equation, not "y=...", but instead you use "x=...".

Like this:

x = 1.5

Every point on the line has x coordinate 1.5,

that is why its equation is x = 1.5

Rise and Run

rise and run

Sometimes the words "rise" and "run" are used.

Rise is how far up

Run is how far along

And so the slope "m" is:

m =  riserun

You might find that easier to remember.

Animation    

Now Play With The Graph !

You can see the effect of different values of m (the slope) and b (the y intercept) at Explore the Straight Line Graph

Step-by-step explanation:

include a picture of the drawing in order for me to

step-by-step explanation: