# Question #35ec7

May 13, 2017

Intercept for $\text{ "y-y=2x" } \to \left(x , y\right) \to \left(0 , - 8\right)$
Intercept for $\text{ "y=2x" } \to \left(x , y\right) = \left(- \frac{8}{5} , - \frac{16}{5}\right)$

#### Explanation:

$\textcolor{b l u e}{\text{Assumption: The question as given is correct}}$

This is an exercise in thinking before you leap.

Consider the equation: $y - y = 2 x$

This is the same as $0 = 2 x \implies x = 0$

Note that $x = 0$ is the y-axis. So the question is really asking:

What is the y-intercept for $3 x + y = - 8$?

Consider: $3 x + y = - 8$

Subtract $3 x$ from both sides

$y = - 3 x - 8$

Set $x = 0$ giving:

$y = - 8$

So the intercept is $\left(x , y\right) \to \left(0 , - 8\right)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Assumption: The question as given is not correct}}$
Suppose the given $y - y = 2 x$ was meant to be $y = 2 x$

Then as instructed in the question: read off the values from the graph:

Intercept for $\text{ } y = 2 x \to \left(x , y\right) = \left(- \frac{8}{5} , - \frac{16}{5}\right)$

These value would be difficult to read off the graph accurately (precise). This implies that $y - y = 2 x$ could be correct.