Question

20 which of the following is an equation of the line whose graph is shown in the coordinate plane below? a $y = -\frac{3}{2}x + 4$ b $y = -\frac{2}{3}x + 4$ c $y = \frac{2}{3}x + 6$ d $y = \frac{3}{2}x + 6$

Explanation:

Step1: Identify two points on the line

We can see from the graph that the line passes through the points \((-3, 6)\) and \((6, 0)\), and also intersects the \(y\)-axis at \((0, 4)\) (so the \(y\)-intercept \(b = 4\)).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's use the points \((-3, 6)\) and \((6, 0)\).
So \(x_1=-3\), \(y_1 = 6\), \(x_2=6\), \(y_2=0\).
Then \(m=\frac{0 - 6}{6-(-3)}=\frac{-6}{9}=-\frac{2}{3}\).

Step3: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.
We found that \(m =-\frac{2}{3}\) and \(b = 4\) (from the point \((0,4)\)).
So the equation of the line is \(y=-\frac{2}{3}x + 4\).

Answer:

B. \(y =-\frac{2}{3}x + 4\)