Question

write an equation in point - slope form for a line that is parallel to
with a slope of \\(\frac{1}{3}\\) and passes through the point \\((-1, -4)\\)

Explanation:

Step1: Recall Point - Slope Formula

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

Step2: Identify the Values of $x_1$, $y_1$ and $m$

We are given the point $(-1,-4)$ and the slope $m = \frac{1}{3}$. So, $x_1=-1$, $y_1 = - 4$ and $m=\frac{1}{3}$.

Step3: Substitute the Values into the Formula

Substitute $x_1=-1$, $y_1=-4$ and $m = \frac{1}{3}$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-4)=\frac{1}{3}(x - (-1))$.
Simplify the left - hand side and the right - hand side: $y + 4=\frac{1}{3}(x + 1)$.

Answer:

The equation in point - slope form is $y + 4=\frac{1}{3}(x + 1)$