Question

Equation of line that passes through (-2,-6) and (1,2)

Answer 1

y =
`(8)/(3)` x -
`(2)/(3)`

Explanation:

y = mx +b

You need the slope and the y intercept

The slope is the change in y over the change in x

(-2,-6) (1,2)

The y's are 2 and -6

The x's are 1 and -1

`(2 - - 6)/(1 - -2))` =
`(2 + 6)/(1 + 2)` =
`(8)/(3)`

the slope (m) is
`(8)/(3)`

We will use this slope and one of the points to find the y-intercept (b) I will use the point (1,2) Either point will work, but this is nicer without the negative signs to deal with.

m =
`(8)/(3)`

x = 1 from the point (1,2)

y = 2 from the point (1,2)

Substitute these all in y = mx + b and solve for b

y = mx + b

2 =
`(8)/(3)`(1) + b

2 =
`(8)/(3)` + b Subtract
`(8)/(3)` from both sides

2 -
`(8)/(3)` = b

`(6)/(3)` -
`(8)/(3)` = b

`(-2)/(3)` = b

y = mx + b

y =
`(8)/(3)` x -
`(2)/(3)`