Question

1. the line shown represents the balance y of bens lunch account. two days ago, he owed $1. what is an equation of the line in point - slope form? circle the letter of the correct answer. a. y - 1 = 2(x + 2) b. y + 1 = -2(x + 2) c. y - 1 = -2(x - 2) d. y + 1 = 2(x + 2)

Explanation:

Step1: Identify the point

Two days ago ($x = - 2$), he owed $1$ dollar, so the point is $(-2,-1)$.

Step2: Find the slope

Pick two points on the line, say $(0, - 5)$ and $(-2,-1)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1-(-5)}{-2 - 0}=\frac{-1 + 5}{-2}=\frac{4}{-2}=-2$.

Step3: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Substituting $m=-2$, $x_1=-2$ and $y_1=-1$ gives $y+1=-2(x + 2)$.

Answer:

B. $y + 1=-2(x + 2)$