Thinking Sideways

Algebra Level 1

Suppose instead of graphing a line as $y = mx + b$ (where $m$ is the slope and $b$ is the $y$ -intercept) we graphed it as $x = Qy + Z .$ (Incidentally, this allows graphing vertical lines in the format.)

What is the relationship between $m$ and $Q?$

m = 1 - \frac{1}{Q}

m = -\frac{1}{Q}

m = \frac{1}{Q}

1 solution

Ram Mohith
Jul 26, 2018

Given : $y = mx + b -----(1)$

$x = Qy + Z$

$\implies Qy = x - Z$

$\implies y = \dfrac{1}{Q}x - \dfrac{Z}{Q} -----(2)$

Now, by comparing the equations (1) and (2) we get :

$m = \dfrac{1}{Q}$

Thinking Sideways

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