Question

How do you write the equation in point slope form given (2, -1), m=-3?

Answer 1

The general point-slope form for linear equations is given as, $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$. It emphasizes the slope of the line and a point on the line (which is not the y-intercept). We will use this formula and substitute the given values in it to get the required equation.

Complete step-by-step solution:
We have been asked to write the equation in point slope form using the given values of (2, -1), m=-3. We know that the point-slope formula is given as, $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$, where $m$ is the slope and $\left( {{x}_{1}},{{y}_{1}} \right)$ is a point through which the line passes. We have been given the slope and the point values, so we can write them as,
${{x}_{1}}=2$
${{y}_{1}}=-1$
And $m=-3$
We will now substitute these values in a point-slope formula. So, we get,
$\Rightarrow y-\left( -1 \right)=-3\left( x-2 \right)$
$\Rightarrow y+1=-3\left( x-2 \right)$
$\Rightarrow y+1=-3x+6$
$\Rightarrow 3x+y=5$
Thus, we get the required linear equation as: $3x+y=5$.

Note: We should know the formula for the general point slope form of a linear equation in order to solve this question. When the values of the points and the slope are given, there is very less chance of an error in solving the above question as we have to simply substitute the values in the formula to get the desired linear equation. The only chances of getting an incorrect answer is by not paying attention to the signs while substituting the values. We should also not get confused with the substitution and substitute the points as (x, y) instead of the $\left( {{x}_{1}},{{y}_{1}} \right)$. By doing so, we will get the incorrect equation.