Question

What is the equation of the line if the line have slope $\frac{1}{3}$ and passing through the point (2,3)?

• A. $\text{y}=\frac{1}{3}\text{x}+\frac{7}{3}$
• B. $\text{y}=\frac{1}{3}\text{x}+\frac{1}{3}$
• C. $\text{y}=\frac{7}{3}\text{x}+\frac{1}{3}$
• D. $\text{y}=\frac{7}{3}\text{x}+\frac{7}{3}$

Answer 1

The correct option is A $\text{y}=\frac{1}{3}\text{x}+\frac{7}{3}$

Given,
Slope of the line = $\frac{1}{3}$

Equation of the line is: $\text{y = mx + c}$

$⟹\text{y}=\frac{1}{3}\text{x}+\text{c}$-------(1)

It is also given that the line passes through the coordinates (2,3).

Substitute the coordinates in the equation (1), we get:

$3=\frac{1}{3}\left(2\right)+\text{c}$

$⟹3=\frac{2}{3}+\text{c}$

$⟹\text{c}=3-\frac{2}{3}$

$⟹\text{c}=\frac{7}{3}$

Hence, the equation is $\text{y}=\frac{1}{3}\text{x}+\frac{7}{3}$.