Question

Slope intercept form (-6,19) and (3,-2)

Answer 1

`y = -(7)/(3)x +5`

Explanation:

The general equation of a line in slope-intercept form is

y = mx + b

where m = slope and b = y-intercept is rise over run

`m = \frac {(y_(2) - y_(1))} {(x_(2) - x_(1))}`

where (x₁, y₁) and (x₂, y₂) are any two points on the line

`m = (-2 - 19)/(3 - (-6))\\\\`

`\\\\m= (-21)/(9)`

`m = -(7)/(3)`

So slope-intercept form is

`y = -(7)/(3)x +b\\\\`

`-2 = -(7)/(3)\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\`

or 7 -2 = b

==> b = 5

`y = -(7)/(3)x +5`