Question

How do you find the equation of the line with point $\left( -3,6 \right)$ and m = -2.

Answer 1

Now we are given with a point $\left( -3,6 \right)$ on the line and slope of the line. Now we will write the equation of the line in slope point form which is $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ where m is the slope of the line and $\left( {{x}_{1}},{{y}_{1}} \right)$ is the point on line. Hence we will write the equation in this form and then simplify the equation.

Complete step by step solution:
Now we are given with a point on the line and slope of the line. We know that the equation of a line is a linear equation in two variables.
We want the equation of the line in general form which is $ax+by+c=0$
Now first we will write the equation in slope point form.
We know that if $\left( {{x}_{1}},{{y}_{1}} \right)$ is the points on the line and if m is the slope of the line then the equation of line in slope point form is given by $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$
Now we have $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,6 \right)$ and m = - 2.
Hence the equation of the line is
$\begin{aligned} & \Rightarrow y-6=-2\left( x-\left( -3 \right) \right) \\\ & \Rightarrow y-6=-2\left( x+3 \right) \\\ \end{aligned}$
Now simplifying the equation and writing it in general form we get,
$\begin{aligned} & \Rightarrow y-6=-2x-6 \\\ & \Rightarrow 2x+y=0 \\\ \end{aligned}$

Hence the equation of the line in general form is $2x+y=0$.

Note: Now note that the intersection of the line with y axis is known as y axis and intersection of line with x axis is called x intercept. We also have slope intercept form of line which is $y=mx+c$ where c is the y intercept of the line. Not to be confused among the different equations of line.