Answer:
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
Explanation: