Question

The equation of the line passing through each of the following pair of points given below in the form $y=mx+c$ is $(0,5)$ and $(5,6)$

• A. $y=\frac{1}{5}x-5$
• B. $y=-\frac{1}{5}x+5$
• C. $y=-\frac{1}{5}x-5$
• D. $y=\frac{1}{5}x+5$

Answer 1

The correct option is D $y=\frac{1}{5}x+5$

The equation of a line passing through two points $(x_1,y_1)$ & $Q(x_2,y_2)$ is $\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$.
The equation of line passing through $(0,5)$ and $(5,6)$ is:
$\frac{y-5}{6-5}=\frac{x-0}{5-0}$
$\Rightarrow 5(y-5)=x$
$\Rightarrow x=5y-25$
$\Rightarrow y=\frac{x+25}{5}$
$\Rightarrow y=\frac{x}{5}+5$