Question

question 10 of 10
which equation describes the same line as $y - 3 = -1(x + 5)$?

a. $y = -1x - 1$

b. $y = -1x - 2$

c. $y = -1x - 5$

d. $y = -1x + 8$

Explanation:

Step1: Expand the right - hand side

We start with the equation \(y - 3=-1(x + 5)\). Using the distributive property \(a(b + c)=ab+ac\), here \(a=-1\), \(b = x\) and \(c = 5\), so \(-1(x + 5)=-x-5\). The equation becomes \(y - 3=-x - 5\).

Step2: Solve for y

To solve for \(y\), we add 3 to both sides of the equation \(y-3=-x - 5\). So \(y=-x - 5+3\).

Step3: Simplify the right - hand side

Simplify \(-x-5 + 3\), we combine the constant terms: \(-5+3=-2\). So \(y=-x - 2\) (which can also be written as \(y=-1x-2\)).

Answer:

B. \(y=-1x - 2\)