Question

Find the slope and $y$-intercept of a line represented by the equation: $x=zy+n$

• A. Slope $=\frac{-n}{z}$
  $y$-intercept $=\frac{1}{z}$
• B. Slope $=\frac{n}{z}$
  $y$-intercept $=\frac{-n}{z}$
• C. Slope $=\frac{1}{z}$
  $y$-intercept $=\frac{-n}{z}$
• D. Slope $z$
  $y$-intercept $=n$

Answer 1

The correct option is C Slope $=\frac{1}{z}$

$y$-intercept $=\frac{-n}{z}$
Given, $x=zy+n$
Convert the given equation into slope intercept form of equation of a line.
$y=mx+b$
Where $m$ is the slope and $b$ is the $y$-intercept of the line.
Simplify the given equation: $x=zy+n$
$x-n=zy$
$y=\frac{x-n}{z}$
$y=\frac{x}{z}-\frac{n}{z}$
$y=\frac{1}{z}\times x-\frac{n}{z}$
On comparing this equation with $y=mx+b$
We get:
Slope = $m=\frac{1}{z}$
$y$-intercept $=b=\frac{-n}{z}$
Option (c) is correct