Question

use point-slope form to write the equation of a line that passes through the point $(-1, 10)$ with slope $\frac{11}{9}$.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line 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 values of $x_1,y_1$ and $m$

We are given the point $(-1,10)$, so $x_1=-1$ and $y_1 = 10$. The slope $m=\frac{11}{9}$.

Step3: Substitute values into the formula

Substitute $x_1=-1$, $y_1 = 10$ and $m=\frac{11}{9}$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 10=\frac{11}{9}(x-(-1))$, which simplifies to $y - 10=\frac{11}{9}(x + 1)$.

Answer:

The equation of the line in point - slope form is $y - 10=\frac{11}{9}(x + 1)$