Question

How do you write an equation for the line that passes through (6,5) and (4,1)?

Answer 1

'The general equation of a line is `y=mx+b` where `m` is the slope and `b` is the intersection where `x=0`.

Explanation:

So you need to calculate `m` and `b`, the formula of the slope is `m=(y_2-y_1)/(x_2-x_1)=(5-1)/(6-4)=4/2=2`.
This formula tells us that for each step you give in x you climb m=2 in y. And now you can solve the equation and obtain `b`, so you take any point the line passes through, (6,5) for example.
`5=2*6+b`
and then
`b=5-12=-7`
And finally you have the line equation
`y=(2)x+(-7)`
graph{2x-7 [-16.75, 23.25, -8.24, 11.76]}