Question

which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
\\( y + 1 = 3x \\)
\\( y = -3x + 1 \\)
\\( y = 3x + 1 \\)
\\( y - 3x = -3 \\)

Explanation:

Step1: Find line's slope-intercept form

First, identify two points on the line: $(0, -1)$ and $(1, 2)$. Calculate slope:
$m=\frac{2-(-1)}{1-0}=3$. The y-intercept $b=-1$, so the line is $y=3x-1$.

Step2: Rewrite each option to $y=mx+b$

• Option1: $y+1=3x$ → $y=3x-1$
• Option2: $y=-3x+1$ (already in form)
• Option3: $y=3x+1$ (already in form)
• Option4: $y-3x=-3$ → $y=3x-3$

Step3: Match to original line

A system has infinite solutions if equations are identical.

Answer:

A. $y+1=3x$