Question

which equation represents the graphed function?
-3x + 2 = y
-\frac{2}{3}x + 2 = y
\frac{3}{2}x - 3 = y
2x - 3 = y

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -3)\) (the y-intercept) and \((2, 0)\) (the x-intercept).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -3)\) and \((2, 0)\), we have \(x_1 = 0,y_1=-3,x_2 = 2,y_2 = 0\).
So \(m=\frac{0 - (-3)}{2 - 0}=\frac{3}{2}\).

Step3: Use slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=\frac{3}{2}\) and from the point \((0,-3)\), the y - intercept \(b=-3\). So the equation of the line is \(y=\frac{3}{2}x-3\), which can be written as \(\frac{3}{2}x - 3=y\).

Answer:

\(\boldsymbol{\frac{3}{2}x - 3=y}\) (corresponding to the option \(\frac{3}{2}x - 3=y\))