Question

Y-4=-3(x+2)


y= -3/2x+1


y-1=-3x


3x+y=1

Answer 1

The second one: y = -3/2x + 1

Hope this helps!

Explanation:

( -2, 4 ) : ( 2, -2 )

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

Slope =
`(-2-4)/(2 - ( -2)) =(-6)/(4) = - (3)/(2)`

y =
`-(3)/(2)x` + 1 ( + 1 is the y-intercept, where the graph intercepts the y axis... )

Answer 2

y = -
`(3)/(2)` x + 1

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m =
`(-2-4)/(2-(-2))` =
`(-6)/(2+2)` =
`(-6)/(4)` = -
`(3)/(2)`

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = -
`(3)/(2)` x + 1 ← equation of line