Question

A line passes through the $y-$axis at $y=3.$ It has a slope of $\frac{1}{3}$. Find the equation of the line.

• A. $3y=x+9$
• B. $3y=x+3$

Answer 1

The correct option is A $3y=x+9$

The given line passes through the $y-$axis at $y=3.$
Hence, the $y-$intercept is 3.

Slope of the line is $\frac{1}{3}$.
$\therefore m=\frac{\text{Rise}}{\text{Run}}=\frac{1}{3}$

The intercept-slope form of straight line is $y=mx+(y-\text{intercept}).$
$\Rightarrow y=\frac{1}{3}x+3$
$\Rightarrow 3y=x+9$