Coordinate geometry

Original post by Magenta96

I have a rough idea about the last one, you can find the gradient of the line which is 2000/1000 = 2, and if you extrapolate that line it intersects the y axis at about (0, 25), I'm not confident about this one though so don't just take my word for it. For the next one, since the lines linear, it'll go in equal steps so couldn't 4000 minutes be $65, since 1000 is $35, 2000 is $45, 3000 could be $55 and 4000, 65? Like I said though, this is a q I'm not too confident with so check to make sure.

This is incorrect. The gradient of the line is delta(y)/delta(x) this is not 2.
The line does however intersect at 25, though:
y-y₁ = m(x - x₁) is a better method of doing this.

Reply 23

Original post by strangepath

I am such an idiot, the answer was written right there :colone:

dw about it, everyone's done it before :smile:

Reply 24

OP

Original post by joostan

This is incorrect. The gradient of the line is delta(y)/delta(x) this is not 2.
The line does however intersect at 25, though:
y-y₁ = m(x - x₁) is a better method of doing this.

Sorry I still find the last question really difficult. :frown:

Reply 25

Original post by strangepath

Sorry I still find the last question really difficult. :frown:

Which part in particular?

Reply 26

OP

Original post by joostan

Which part in particular?

the whole question I guess. If you could give formulas or make it into an equation then I might be able to do it.

Reply 27

Original post by strangepath

the whole question I guess. If you could give formulas or make it into an equation then I might be able to do it.

\ m = \frac{\Delta y}{\Delta x}

After calculating the gradient use:

\ y - y_1 = m(x - x_1)

to find the y-intercept by rearranging into the format y=mx+c

Reply 28

OP

I am sorry I just don't get it. I don't know what I should put into the formula. Please help this dumb guy out, I need to due it tomorrow. :redface:

Reply 29

Original post by strangepath

I am sorry I just don't get it. I don't know what I should put into the formula. Please help this dumb guy out, I need to due it tomorrow. :redface:

Quoting me makes it easier to spot :tongue:

and don't put yourself down :mad:

Now: What is

\Delta y

Reply 30

OP

Original post by joostan

Quoting me makes it easier to spot :tongue:

and don't put yourself down :mad:

Now: What is

\Delta y

is it 45-35?

Reply 31

Robbie242

Original post by strangepath

I am sorry I just don't get it. I don't know what I should put into the formula. Please help this dumb guy out, I need to due it tomorrow. :redface:

\ m = \frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}

Change in y, over change in x with coordinates

(x_1,y_1)

and

(x_2,y_2)

Reply 32

Original post by strangepath

is it 45-35?

Yes - what about

\Delta x

?

Reply 33

OP

Original post by Robbie242

\ m = \frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}

Change in y, over change in x with coordinates

(x_1,y_1)

and

(x_2,y_2)

so its m = 45-35/2000-1000
which is m = 0.01?

Reply 34

Original post by strangepath

so its m = 45-35/2000-1000
which is m = 0.01?

yes though writing it as a fraction is better notation :smile:

Reply 35

Robbie242

Original post by strangepath

so its m = 45-35/2000-1000
which is m = 0.01?

Precisely now proceed by plugging the coordinates and gradient (m) into the straight line equation

y-y_1=m(x-x_1)

Remember, you can chose either points, but go with the simpler ones!

(edited 11 years ago)

Reply 36

OP

Original post by joostan

\ m = \frac{\Delta y}{\Delta x}

After calculating the gradient use:

\ y - y_1 = m(x - x_1)

to find the y-intercept by rearranging into the format y=mx+c

what is the y and x without the number one attached to it?

Reply 37

Robbie242

Original post by strangepath

what is the y and x without the number one attached to it?

They are just algebraic constants, so say you have coordinates (2,3) and m=1

y-3=1(x-2)[br]y-3=x-2[br]y=x+1

Reply 38

Original post by strangepath

what is the y and x without the number one attached to it?

Pick either point (35,1000) or (45,2000)
These points have both an x-coordinate and a y-coordinate.
So a general point on the line can be said to be the point:

\ (x_1 , y_1)

The 1 just makes it a general term.

Reply 39

OP