Question

write the slope intercept form of the equation with the given characteristic passes through (2,-2) & (4,1)

Answer 1

`y = (3)/(2)x - 5`

Explanation:

General format for the slope-intercept form of an equation:

`y = mx + c`

where:

m = slope

c = y-intercept

`(x_(1) , y_(1))` =
`(2, -2)`

`(x_(2) ,y_(2))` =
`(4, 1)`

m =
`(y_(2) -y_(1))/(x_(2) - x_(1))`

=
`(1- (-2))/(4-2)`

=
`(1+2)/(2)`

m =
`(3)/(2)`

Substituting this value of m into our equation:

`y = (3)/(2)x + c`

Substituting the coordinates of any of the two points into the above equation to solve for c:

1 =
`(3)/(2)`(4) + c

1 =
`(12)/(2)` + c

1 = 6 + c

Isolate c and make it the subject of the equation:

c =
`1 -6`

c =
`-5`

∴The slope-intercept form of the equation after substituting the calculated values of m and c:

`y = (3)/(2)x + (-5)`

`y = (3)/(2)x - 5`