Question

which equation best represents the relationship between x and y in the graph? a. y = 4x + 1 b. x=\frac{1}{4}y + 1 c. y=\frac{1}{4}x - 1 d. y =-\frac{1}{4}x - 1

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: Determine y - intercept

The line crosses the y - axis at $y=-1$, so $b = - 1$.

Step3: Calculate the slope

Pick two points, say $(0,-1)$ and $(4,-2)$. Slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2+1}{4 - 0}=-\frac{1}{4}$.

Step4: Write the equation

Substitute $m =-\frac{1}{4}$ and $b=-1$ into $y=mx + b$, we get $y=-\frac{1}{4}x-1$.

Answer:

D. $y =-\frac{1}{4}x - 1$