how do i prove the graph of a linear equation is a line? i know the slope between every point should be the same but idk how to prove it with letters. the equation is y=3/2x-9/2 but it should work with any equation i guess.

Answer 1

easy way: it's called a linear function for a reason.

or, you can show that the slope of the function is a constant 3/2 between any two points, so the graph has no curves or bends in it.

Answer 2

thanks. how do you underline the text?
i dont understand why you talk about functions but i find

say the coordinate are x1 y1, x2 y2
3/2=y1-y2 / x1-x2
= 3/2x1 - 3/2x2 / x1-x2
=3/2

it is a loop. how do i prove it pls?

Answer 3

to underline, use html tag < u> ... </ u>
(omit the space after the "<"
There's also < b> for bold and < i> for italic.
More general tags are filtered out, but these three can help.
There are also < sub> for subscripts and < sup> for superscripts (exponents)

To prove the slope of the graph is constant, just pick any two points (x1,y1) and (x2,y2) on the graph. The slope is, as usual (y2-y1)/(x2-x1).

Now, since y = 3/2 x - 9/2, that gives you
((3/2 x2 - 9/2) - (3/2 x1 - 9/2))/(x2-x1)
= (3/2 x2 - 3/2 x1)/(x2-x1)
= 3/2 (x2-x1)/(x2-x1)
= 3/2
no matter which two points you choose. So, the slope is the same everywhere.

Answer 4

thank you i see it now