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Parallel lines always have to have the same gradient.
(?x)
For example: y = 3x + 2 is parallel to y = 3x + 5
For perpendicular lines, one has to
be positive and one has to be
negative.
For example, if one line was y = 3x + 2 then the
perpendicular line would be y = -1/3 + 2. It doesn't matter
what the y-intercept is because n matter where on the y
axis is, the angle will always be the same.
The way to work this out is: If one line has the gradient m, any perpendicular line will have the
gradient -1/m. So, y = mx + c is perpendicular to y = -1/mx + c Basically all you have to do is put
either a -/+ 1 over the original gradient plus a y-intercept.
A y-intercept is when the line meets the y
axis.
For example, if the line meets the y axis at 1 (like the one in the picture below), the y-intercept will
be 1.
Linear
Functions
f(x)=, f:x ---> and x-----> all are the same. They all
mean y=_________ when you make a y = mx + c
equation.
This is because they all mean the function
of x
Working out the equation of
a line
To work out the equation of a line, you need
to work out the difference of y divided by the
difference of x. Then you add the y-intercept. It should be in the form of y = mx + c
For example, on the graph, two points have been marked on
the line. to work out the equation of a line, you need to count
how much you go left or right and how much you go up or
down. REMEMBER TO ALWAYS COUNT ON THE RIGHT HAND
SIDE OF THE LINE. In the graph, you go right 2 spaces and up 2
spaces. 2/2 = 1 Therefore te gradient is one. The next step is to
work out the y-intercept which has been shown below. you
the write it as an equation. y = x + 1 (x is the gradient)
When you are given 2 co-ordinates from the line
When you are given 2 co-ordinates and are asked to work out the
equation of the line, all you have to do is think of the two
co-ordinates as your two points.
For example, if you had the co-ordinates (2,2) and (4,6), you could
use these as your points. REMEBER THAT IT IS THE DIFFERENCE OF Y
DIVIDED BY THE DIFFERENCE OF X.
To work out the difference of x and y, you just need to remember that a co-ordinate is formed like this: (x,y). So, in the example
above, you would do 4 - 2 = 2 to give you the difference of x and do 6 - 2 = 4 to give you the difference of y. You would then do 4/2 =
2/1 = 2. Therefore 2 would be your gradient. To work out the y-intercept, you would have to think that for every 2 you went up, you
went 1 right. Therefore, for every 2 you go down you must go 1 down. you are trying to find a co-ordinate where the x part is 0. So,
if I go, 2 left from (2,2) I must go 4 down as well. that would give me the co-ordinate (0,-2). the y part of the cordinate would be my
y-intercept so the equation of the line would be y = 2x -2.