Question

What is the point-slope form of a line that has a slope of $3$ and passes through the point $\left(-1,4\right)$?

• A. $y-\left(-1\right)=5\left(x-4\right)$
• B. $4-y_1=3\left(-1-x_1\right)$
• C. $y-3=-1\left[\left(x-\left(-4\right)\right)\right]$
• D. $y-4=3\left[\left(x-\left(-1\right)\right)\right]$

Answer 1

The correct option is D

$y-4=3\left[\left(x-\left(-1\right)\right)\right]$

Explanation for correct option:

Option(D):

Given the slope is $3$ and passes through the point $\left(-1,4\right)$.

We know slope of a point is given by

$m=\frac{y-y_1}{x-x_1}$

Substitute $3$ for $m$, $-1$ for $x_1$ and $4$ for $y_1$ in $m=\frac{y-y_1}{x-x_1}$, we get

$$\begin{gathered} 3=\frac{y-4}{x-\left(-1\right)} \\ \therefore y-4=3\left[\left(x-\left(-1\right)\right)\right] \end{gathered}$$

The required equation of the line is $y-4=3\left[\left(x-\left(-1\right)\right)\right]$.

Hence, option D is correct.