Question

Hello, I need the steps. I'm kinda confused. Thanks!

Answer 1

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

Explanation:

The general form of the equation of the line (linear equation) is:

y = ax + b

The line passes through (-3, -1) and (6, -7), i.e:

(1) (x=-3, y=-1) is a point that verifies the equation of the line, and

(2) (x=6, y=-7) also verifies the equation.

So we can put up a system of 2 equations to obtain a and b:

y = ax + b

(1) -1 = a (-3) + b

(2) -7 = a (6) + b

______________

substracting (1) - (2) we can obtain a:

-1 - (-7) = a (-3-6) ⇒ 6 = -9 a ⇒ a = -2/3

by replacing a in (1) we can obtain b:

-1 = -2/3 (-3) + b ⇒ -1 -2 = b ⇒ b = -3

so, the equation is: y = ax + b ⇒ y = -2/3 x - 3

Verification: (2) giving x= 6, let's see if y=-7 is obtained:

y = -2/3 6 - 3 ⇒ y = -4 - 3 = 7 ⇒ RIGHT!

Answer 2

First find slope: (y2-y1)/(x2-x1)
The points: (-3,-1), (6,-7)
(-7+1)/(6+3) = -6/9 = -2/3
Use equation: y = mx + b
y = -2/3x + b
Plot in any point
-1 = -2/3(-3) + b
-1 = 2 + b, b = -3
Final equation in slope intercept form:
Y = -2/3x -3