Question

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

Answer 1

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 $m=m$

& \Rightarrow y-0=m(x-0) \\\ & \Rightarrow y=mx \\\ \end{aligned}$$ Hence, $$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.