Question

choose the correct equation for the red line pictured below
o y = (3/2)x -1
o y= (-2/3)x -1
o y= (-3/2)x +1
o y= -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: Find the y - intercept

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

Step3: Calculate the slope

Pick two points on the line, say $(-2,2)$ and $(0, - 1)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - 2}{0+2}=\frac{-3}{2}$.

Step4: Write the equation

Substitute $m =-\frac{3}{2}$ and $b=-1$ into $y = mx + b$, we get $y=-\frac{3}{2}x - 1$.

Answer:

$y=(-3/2)x - 1$ (corresponding to the third option in the multiple - choice list)