Question

question 3
problem #3 was also hard for eddie. eddie was supposed to use a slope of \\(\frac{1}{3}\\) and the point (-3,12) to graph the equation of a line. his graph is shown below. gerald informed eddie that this graph is also incorrect. which graph should eddie have drawn?

Explanation:

Step1: Find the correct equation

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We know the slope $m=\frac{1}{3}$ and the point $(-3,12)$. Substitute into the equation:
$12=\frac{1}{3}(-3)+b$
$12 = - 1 + b$
$b = 13$. So the equation is $y=\frac{1}{3}x + 13$.

Step2: Analyze the graph

We need to check which graph has a slope of $\frac{1}{3}$ (rising 1 unit for every 3 units right) and passes through $(-3,12)$ or has y-intercept 13. The incorrect graph (Eddie's) likely has wrong slope or intercept. The correct graph should match the equation $y=\frac{1}{3}x + 13$. (Since the options aren't fully visible, but the process is: use point - slope to find the correct line's equation, then identify the graph with slope $\frac{1}{3}$ and y - intercept 13.)

Answer:

(Assuming the correct graph is identified by its slope and intercept; since the original graph is incorrect, the correct one has slope $\frac{1}{3}$, y - intercept 13, and passes through $(-3,12)$. The specific graph would be the one with these properties, e.g., if options are graphs, the one with slope $\frac{1}{3}$ and y - intercept 13.)