Question

a line that includes the point (10, -10) has a slope of \\(\frac{1}{3}\\). what is its equation in point - slope form?
use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.
\\(y - \square = \square (x - \square)\\)

Explanation:

Step1: Recall point - slope form

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

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

We are given that the point $(x_1,y_1)=(10, - 10)$ and the slope $m = \frac{1}{3}$.

Step3: Substitute values into point - slope form

Substitute $x_1 = 10$, $y_1=-10$ and $m=\frac{1}{3}$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-10)=\frac{1}{3}(x - 10)$, which simplifies to $y + 10=\frac{1}{3}(x - 10)$. But in the given format, we have $y-\square=\square(x - \square)$. Since $y-(-10)=y + 10$, the first blank is $- 10$, the second blank is $\frac{1}{3}$ and the third blank is $10$.

Answer:

$y-(-10)=\frac{1}{3}(x - 10)$ (or filling in the blanks: the first blank is - 10, the second blank is $\frac{1}{3}$, the third blank is 10)