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What is the equation of a straight line graph?

By Filsan on the 10th of January, 2013

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Equation of a Straight Line

The equation of a straight line is usually written this way:

y = mx + b

What does it stand for?

y = how far up

x = how far along

m = Slope or Gradient (how steep the line is)

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

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:
m  =   Change in Y Change in X

Example 1

m  =   2 1
=  2

b = 1 (where the line crosses the Y-Axis)
 Therefore 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

Example 2

m  =   3 -1
=  –3

b = 0

This gives us y = –3x + 0
We do not need the zero!

 Therefore y = –3x

Example 3: Vertical Line

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’s why its equation is x = 1.5

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  =   rise run

You might find that easier to remember

By Dawn Lubka on the 16th of January, 2013

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There are three functions that give us a straight line when we graph them.

y=mx+b

This function can be graphed using the rise and run method where b is your starting point and m is your rise/running number. M can be expressed as a whole, 3, or a fraction, 3/4. Whole numbers will always run 1. Fractions the numerator is your rising number and the demoninator is your running number. If m is positive then you run to the right, if its negitive you run to the left.

y= a number

This is a horizontal line at that value. It translates into all x values have that y as an answer

x= a number

This is a vertical line at the vaule. It translates to all y values of have the same x.

By Lini on the 19th of January, 2013

Simplify expressions with surds into the form a + b3

Be warned this topic is Chuck Norris hard. Make sure you've done the related topics below before you try and get your head round this one...

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So if you put a square root sign around a number that is not a square number, then what you have written is a surd.

e.g. √10 is a surd, because 10 is not a square number. √9 is not a surd, because 9 is a square number, so you can write √9= 3

Even if the number under the square root sign is not a square number, it can still be simplified.

Write the starting number as a product of two new numbers, where one of them is a square number (e.g. 45 -> 9 x 5).  Take the root of the square number, and write it outside of the root sign

e.g. √45 = √(9×5)=3√5

Follow the links below to see how this topic has appeared in past exam papers

AQA Unit 2 March 2011 (H) - Page 11, Question 17

Other Relates Topics…

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