Question

Find the equation of the line passing through \[(0,0)\] with slope $m$

Answer 1

Hint: The equation of line passing through \[({{x}_{1}},{{y}_{1}})\] and whose slope is $m$ can be found out by point slope form which is given by:
\[y-{{y}_{1}}=m(x-{{x}_{1}})\]

Complete step-by-step solution:
We know the slope and a point on the line, so we can use the point-slope form to get the equation of the line.
According to question: \[{{x}_{1}}=0\] , \[{{y}_{1}}=0\] and \[m=m\]
\[\begin{align}
  & \Rightarrow y-0=m(x-0) \\
 & \Rightarrow y=mx \\
\end{align}\]
Hence, \[y=mx\] is the line which passes through \[(0,0)\] and have slope $m$
Graph below shows a line \[y=x\] , so we can say that a line of the form \[y=mx\] passes through origin and makes some angle with the x axis which depends on the value of slope $m$

Note: There are various methods to get the equation of line such as point-slope form, intercept form, and two-point form. So, we should choose a method as per the data available to us, like here in this question one point and the slope was given so we used point-slope form. You might also make a mistake while writing the formula as \[y+{{y}_{1}}=m(x+{{x}_{1}})\], here in this question, it wouldn’t have affected our answer but it might affect the answer in other questions.
We also have a shortcut method to solve this question, we know that the equation of the line passing through the origin and having slope $m$ is \[y=mx\]. So, we can jump directly to the answer from this fact. You can even verify your answer by putting the point \[(0,0)\] to make sure that the equation satisfies the points.