Answer:
y = -3x - 6
Step-by-step explanation:
first, find the slope
(-4, 6)
(1, -9)
remember the equation for the slope
[tex]\frac{y_{2}-y_{1}}{x_{2} - x_{1}} }[/tex]
insert given points
[tex]x_{1} = -4\\y_{1} = 6\\\\x_{2} = 1\\y_{2} = -9[/tex]
((-9) - (6)) / ((1) - (-4))
simplify
( -9 - 6) / (1 + 4)
= -15/ 5
= -3
now insert it into the equation of the line
remember, the equation of the line is
y = mx + b
where "m" is the slope
and "b" is the y-intercept
to find "b", you just have to plug in a point that is found on the line
we know that (-4, 6) and (1. -9) is found on the line, so let's just use (-4, 6) for this problem
y = mx + b
substitute in the slope of this line
y = -3x + b
now substitute in the given points
6 = -3 * -4 + b
and solve it like any algebra problem, by inverse operations and simplifying
6 = 12 + b
-12 -12
-6 = b
so the equation of the line is
y = -3x -6
