I have the question "Write down the equation of the line passing through the origin and perpendicular to y = 2X + 3".
I know that the equation of a line is y = mx + c and that the origin is (0,0). However, I am not sure how I would start this.
$\endgroup$3 Answers
$\begingroup$An important fact about lines is that they are perpendicular if and only if the slope of one is the opposite reciprocal of the slope of the other. That is, $y=mx+b$ and $y=nx+c$ are perpendicular if and only if $m=-\frac{1}{n}$ (equivalently, $n=-\frac{1}{m}$.
You want your line to be perpendicular to $y=2x+3$, so your line must have slope $m=-\frac{1}{2}$.
Then you have an equation of the form $y=-\frac{1}{2}x+c$, and you need to solve for $c$. To do this, use the fact that your line goes through $(0,0)$. If you plug in $x=0$ and $y=0$ to the equation of the line, you can solve for $c$.
$\endgroup$ $\begingroup$If the line passes through the origin, then you know that $(0,0)$ is on the line.
If the line is perpendicular to $y = 2x+3$ then we know the line has slope $m = -0.5$. This is the negative reciprocal of the slope.
The solution can be obtained by solving $y = -0.5x +b$ using the information given.
It is also worth knowing that if the line passes through the origin, the y intercept is already determined (it is 0 since the line will pass through the y axis at 0).
$\endgroup$ 3 $\begingroup$Hint:
if the line passes thorough the origin than $c=0$ ( substitute $(0,0)$ in your equation).
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