Question

which equation describes the line graphed above? a. $y = \frac{3}{2}x - 6$ b. $y = \frac{2}{3}x - 6$ c. $y = \frac{3}{2}x + 4$ d. $y = \frac{2}{3}x + 4$

Explanation:

Step1: Identify the y-intercept

The line crosses the y - axis at (0, 4), so the y - intercept \(b = 4\). This eliminates options A and B since their y - intercepts are - 6.

Step2: Calculate the slope

We can use two points on the line. Let's take (0, 4) and (- 6, 0) (we can find another point by looking at the graph). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using (0, 4) as \((x_1,y_1)\) and (- 6, 0) as \((x_2,y_2)\), we have \(m=\frac{0 - 4}{-6 - 0}=\frac{- 4}{-6}=\frac{2}{3}\).

Step3: Write the equation

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

Answer:

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