Question

question 4 of 10
what is the point - slope form of a line with slope \\(\frac{2}{5}\\) that contains the point \\((-3, 6)\\)?
\\(\bigcirc\\) a. \\(y + 6 = \frac{2}{5}(x + 3)\\)
\\(\bigcirc\\) b. \\(y - 6 = -\frac{2}{5}(x + 3)\\)
\\(\bigcirc\\) c. \\(y - 3 = \frac{2}{5}(x + 3)\\)
\\(\bigcirc\\) d. \\(y - 6 = \frac{2}{5}(x + 3)\\)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is given by the formula $y - y_1=m(x - x_1)$, where $m$ is the slope of the line and $(x_1,y_1)$ is a point on the line.

Step2: Identify values of $m$, $x_1$ and $y_1$

We are given that the slope $m=\frac{2}{5}$ and the point on the line is $(-3,6)$. So, $x_1=-3$ and $y_1 = 6$.

Step3: Substitute values into the formula

Substitute $m=\frac{2}{5}$, $x_1=-3$ and $y_1 = 6$ into the point - slope formula $y - y_1=m(x - x_1)$.
We know that $x - x_1=x-(-3)=x + 3$ and $y - y_1=y - 6$. And $m=\frac{2}{5}$.
So the equation becomes $y - 6=\frac{2}{5}(x+3)$.

Answer:

D. $y - 6=\frac{2}{5}(x + 3)$