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Higher Mathematics - Unit 1, part 1, The Straight Line

Higher Mathematics – The Straight Line

/ = divided by

Gradient:

“Gradient is a number that measures the slope of a line. Divide the vertical distance by the horizontal distance.

D (up/down) / D (along)

The notation for the gradient is ‘m’ -> Mab = the gradient of line ab!

The basic formula for the gradient is;

Y1-y2 / x2-x1

Example:

Find the gradient of line AB, where A = (2,4) and B = (5,9)

M = b1-b2 / a1-a2

= 4-9 / 2-5

=-5 / -3

= 1.66

Any two lines which share a common gradient are parallel.

Any two lines which have a value of -1 when their respective gradients are multiplied, are perpendicular.

A straight line has the equation; y = m x + c

Y = the ‘y’ value

M = the gradient

X = the ‘x’ value

C = the ‘y’ intercept

If you know the equation of a line, then you can find the x or y value by setting the x or y value to 0 respectively.

I.e. to find y, set x = 0 (and vice versa)

To find the distance of a straight line when we know any two points on the line, we can use the ‘distance formula’:

AB = the square root of; (a2-a1)^2 + (b2-b1)^2 – where ^2 = squared

If we know two points on a straight line then we can work out the midpoint between those two points;

= (a1 - a2 / 2 , b1 – b2 / 2)

In simpler form, the midpoint is (difference between the two a values, difference between the two b values)

Special Lines in a Triangle:

Median: joins a vertex to a midpoint on the opposite side

Altitude: is a line through a vertex perpendicular to the opposite side

The 3 medians of a triangle meet it ‘G’, the centroid of the triangle.

About the Author

Liam Hayman is a 16-years-old school kid - just your average school kid. This is why he views his articles based on mostly teen issues to be of value because they are from the eyes of a current teenager!

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