Question

1. which equation represents the relationship between the independent and dependent variables? a. y=-5x - 1 b. y = 15x - 1 c. y=-5x + 5 d. y=-x - 5

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate the slope $m$ using two points

Use the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0, - 1)$ and $(x_2,y_2)=(3,-16)$. Then $m=\frac{-16-( - 1)}{3 - 0}=\frac{-16 + 1}{3}=\frac{-15}{3}=-5$.

Step3: Find the y - intercept $b$

When $x = 0$, $y=-1$. In the equation $y=mx + b$, substituting $x = 0$ gives $y=b$. So $b=-1$.

Step4: Write the equation

The equation of the line is $y=-5x - 1$.

Answer:

A. $y=-5x - 1$