Question

Find the equation of the line whose slope and y-intercept are given Slope$=\frac{-2}{3}$, y-intercept$=\frac{1}{2}$.

Answer 1

We know that the equation of a line is $y=mx+c$ where $m$ is the slope of the line and $c$ is the y-intercept.

Therefore, with slope $m=-\frac{2}{3}$ and y-intercept $c=\frac{1}{2}$, the equation of a line is:

$y=mx+c\Rightarrow y=(-\frac{2}{3}\times x)+\frac{1}{2}\Rightarrow y=-\frac{2}{3}x+\frac{1}{2}\Rightarrow y=\frac{(-2\times 2x)+3}{6}\Rightarrow y=\frac{-4x+3}{6}\Rightarrow 6y=-4x+3\Rightarrow 4x+6y-3=0$

Hence, the equation of a line is $4x+6y-3=0$.