*
Slope orGradienty when x=0(watch Y Intercept)

How execute you discover "m" and "b"?

b is easy: just check out wright here the line crosses the Y axis.m (the Slope) needs some calculation:
m=Change in YChange in X
*

Knowing this we deserve to job-related out the equation of a directly line:


Example 1

*

m = 21 = 2

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

So: y = 2x + 1


With that equation you have the right to now ...

You are watching: Find m<1

... choose any kind of worth for x and discover the equivalent value for y

For example, as soon as x is 1:

y = 2×1 + 1 = 3

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

Or we might select another value for x, such as 7:

y = 2×7 + 1 = 15

And so as soon as x=7 you will certainly have actually y=15


Positive or Negative Slope?

Going from left-to-best, the cyclist hregarding Push on a Positive Slope:

*
*
*


Example 2

*

m = −31 = −3

b = 0This gives us y = −3x + 0

We carry out not require the zero!

So: y = −3x


*

What is the equation for a vertical line?The slope is undefined ... and wbelow does it cross the Y-Axis?

In truth, this is a distinct case, and you use a different equation, not "y=...", however instead you use "x=...".

Like this:

x = 1.5

Eincredibly suggest on the line has x coordinate 1.5,that is why its equation is x = 1.5


Rise and Run

*

Sometimes the words "rise" and also "run" are offered.

Rise is exactly how far upRun is exactly how much along

And so the slope "m" is:

m = rise run

You could discover that easier to remember.

See more: Flights To Kauai From Lax - Flights From Los Angeles (Lax) To Lihue (Kauai)

*

Now Play With The Graph !

You deserve to check out the impact of various worths of m (the slope) and b (the y intercept) at Explore the Straight Line Graph

Other Forms

We have been looking at the "slope-intercept" form. The equation of a directly line deserve to be composed in many various other ways.

Another well-known create is the Point-Slope Equation of a Straight Line.


Country Note:

Different Countries teach various "notation" (as sent out to me by sort readers):

In the US, Australia, Canada, Eritrea, Iran, Mexico, Portugal, Philippines and also Saudi Arabia the notation is: y = mx + b
In the UK, Australia (also), Bahamas, Bangladesh, Belgium, Brunei, Bulgaria, Cyprus, Egypt, Germany, Ghana, India, Indonesia, Ireland, Jamaica, Kenya, Kuwait, Malaysia, Malawi, Malta, Nepal, New Zealand, Nigeria, Omale, Pakistan, Peru, Singapore, Solomon Islands, South Africa, Sri Lanka, Turkey, UAE, Zambia and also Zimbabwey = mx + c
In Afghanistan, Albania, Algeria, Brazil, China, Czech Republic, Dennote, Ethiopia, France, Lebanon, Netherlands, Kosovo, Kyrgyzstan, Norway, Poland also, Romania, South Korea, Surinam, Spain, Tunisia and also Viet Nam:y = ax + b
In Azerbaijan, China, Finland also, Russia and Ukraine:y = kx + b
In Greece:ψ = αχ + β
In Italy:y = mx + q
In Japan:y = mx + d
In Cuba and also Israel:y = mx + n
In Romania:y = gA + C
In Latby means of and also Sweden:y = kx + m
In Serbia and Slovenia:y = kx + n
In your country: let us know!

... yet it all indicates the very same thing, just different letters.


Slope (Gradient) of a Straight Line Y Intercept of a Straight Line Test Yourself Explore the Straight Line Graph Straight Line Graph Calculator Graph Index