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: Where the line crosses the Y axis.
m (the Slope) needs some calculation:


m = Change in Y/Change in X

Given the slope m and "y intercept" b, the equation of the line is y = m x + b

Given the slope of the line m and one point P1 = (x1,y1) through which the line passes, we can formulate the equation as as: (y- y1)/(x-x1)= m

We have written this equation in a form which makes it clear that the slope calculated between any point (x,y) on the line and the given point P1 is the same. However, the relationship generally gets simplified algebraically to: y = m (x-x1)+ y1

This form is tidier, but conceals the simple truth behind how the equation was crafted, namely as a statement about the slope of the line. Given that the line passes through the two points P1 = (x1,y1) and P2 = (x2,y2), we first find that the slope of the line is
slope: m = (y2- y1)/ (x2-x1)


Example 1 : Find the equation of a straight line through the point (-1,3) with slope 2.

Answer: The slope of the line must be the same between any two points, e.g. between (x,y) and (-1,3) so that

y-3 / x - (-1) = 2

This implies that
y - 3 =2 (x + 1), Hence y = 2x + 5

Continued...

Hello,
Thank you for your valuable input regarding ability portion . Actually I have a social science background and doing my MS psychology , lacking strong foundation for applied sciences I really want to know about books from which I could start my preparation and clearify my concepts which are quiet ambigious in mind as it was read 8 years before,

Thank you.

Assalam-o-aikum
Sir, could you recommend any good detailed book or website for preparing tests related to General ability?

Walikum Salaam For basics you can consult mathematics course books of 8th, 9th and 10th class. For a bit advance level of basics consult GRE Math.

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