Question

How do you draw the line with the slope $m=-2$ and y intercept 0?

Answer 1

Hint: We first take the general equation of a line where we have the slope and y intercept form as $y=mx+c$. We put the given values of slope $m=-2$ and y intercept 0. Then we place the equation in the graph to visualise its intercept form. We can see that the graph passes through $\left( 0,0 \right)$.

Complete step by step solution:
We take the general equation of the line with the slope $m$ as $y=mx+c$.
It’s given that the value form for our required line is $-2$.
Putting the value in the equation of $y=mx+c$, we get $y=-2x+c$.
As the y intercept 0. That’s why the line passes through $\left( 0,0 \right)$.
Putting the value in the equation $y=-2x+c$, we get $0=\left( -2 \right)\times 0+c$.
This gives $c=0$.
The final equation of the line becomes $y=-2x$.

Note: For this equation $y=-2x$ we can convert it into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the form we get that the x intercept, and y intercept of the line will be p and q respectively.
The given equation is $y=-2x$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{align}
  & y=-2x \\
 & \Rightarrow y+2x=0 \\
 & \Rightarrow \dfrac{2x}{0}+\dfrac{y}{0}=1 \\
\end{align}$
The form is indeterminate which gives that the intercept value is 0 and it passes through $\left( 0,0 \right)$.