Math Is Fun Forum

Monique

Member

Registered: 2007-02-17

Posts: 22

gradient and y-intercept

Hi guys!!!

1)
how would I find the gradient and y-intercept of the line when the y line starts from o to 1 to 2 to 3 and from 0 to  -1 to -2  to -3.

The x line goes  from 0 to 2 to 4 to 6 to 8 and from 0 to -2 to -4 to -6 to -8.
A line passes through 4 on the x line and -1 on the y line.??????

after this once the gradient and y-intercept has been found how would I write the equation of the line that passes through 4 on the x line and -1 on the y line

2)
a)  how would I find the gradients of each of these lines

i)   y = 3x + 12

ii)  2y - 6x = 2

b)  why do these lines not have a point of intersection? how would I justify this answer??

all this is making my head spin

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: gradient and y-intercept

1. When you have a line whose equation is y = mx + c,  m is the gradient and c is the y-intercept. For example, for the line given by y = 2x + 3, the gradient is 2 and the y-intercept is 3 (i.e. it passes through the point (0.3)).

If a line passes through the points (a,b) and (c,d), the gradient of the line is (b−d)∕(a−c).

In your example, your line passes through (4.0) and (0,−1). The gradient is therefore (0−(−1))∕(4−0) = 1⁄4.

Since the line passes through (0,−1), the y-intercept is −1.

So the equation of your line is y = {gradient}x + {y-intercept} = (1⁄4)x − 1.

2. If the equation you are given is not in the form y = mx + c, you must write it in that form so the gradient can be read. For example, if you are given x + y = 4 , you must re-write it as y = −x + 4; then you can see that the gradient is −1.

(a) In your example, (i) is already in the form y = mx + c. You can read the gradient straightaway. (ii) is not, so you must re-write it in the form y = mx + c.

(b) If two straight lines do not intersect, that means they are parallel. Parallel lines have the same gradient. Thus, if you have a line with equation y = mx + c and another line with equation y = mx + d, and c ≠ d, then the two lines are parallel; they will never intersect.

I hope you can digest all this. If not, read it through slowly, bit by bit.

Last edited by JaneFairfax (2007-03-09 15:00:04)

Monique

Member

Registered: 2007-02-17

Posts: 22

Re: gradient and y-intercept

thankyou so much Jane.