Question

question 10
4.3 hw #2 mh
$3y - 6 = 2x$
a)
graph of a line
b)
graph of a line

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $3y - 6 = 2x$ to $y=mx+b$:
$$3y = 2x + 6$$
$$y = \frac{2}{3}x + 2$$

Step2: Identify slope and intercept

Slope $m=\frac{2}{3}$ (positive, line rises right), y-intercept $b=2$ (crosses y-axis at $(0,2)$).

Step3: Match to graph

Graph A has positive slope and crosses y-axis below origin? No, correction: Check intercept again. Wait, $y=\frac{2}{3}x+2$: when $x=0$, $y=2$ (above origin). Wait, graph A: let's check x-intercept: set $y=0$, $0=\frac{2}{3}x+2$ → $x=-3$. So line passes through $(0,2)$ and $(-3,0)$? No, wait $3y-6=2x$: when $y=0$, $-6=2x$ → $x=-3$. When $x=0$, $3y=6$ → $y=2$. So line goes through $(-3,0)$ and $(0,2)$, which is a line with positive slope, matching Graph A (since Graph A rises from left to right, and crosses x-axis at negative x, y-axis at positive y? Wait the initial graph A: the line crosses y-axis below? No, maybe misread. Wait no: $y=\frac{2}{3}x+2$: positive slope, y-intercept +2. So the line should cross y-axis at (0,2) (above origin) and x-axis at (-3,0) (left of origin). Graph A shows a line that crosses y-axis below? No, wait maybe the graph A's line: let's see, if x=3, y= (2/3)*3 +2= 4, so (3,4) is on the line, which is right and up. Graph A has a line going up to the right, which matches positive slope. Graph B has negative slope, which is wrong. So Graph A is correct.

Answer:

A) [The graph with a positively sloped line passing through (-3, 0) and (0, 2)]