alejandra correctly wrote the equation $y - 3 = \\frac{1}{5}(x - 10)$ to represent a line that her teacher…

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 the Point and New Slope

From the original equation $y - 3=\frac{1}{5}(x - 10)$, we can see that the line passes through the point $(x_1,y_1)=(10,3)$ and has a slope $m = \frac{1}{5}$. The new line has the same point $(10,3)$ (since it still goes through the same point) and a new slope $m = 2$.

Step3: Substitute into Point - Slope Form

Using the point - slope form $y - y_1=m(x - x_1)$ with $x_1 = 10$, $y_1=3$ and $m = 2$, we get $y - 3=2(x - 10)$.

Answer:

$y - 3 = 2(x - 10)$ (the fourth option: $y - 3 = 2(x - 10)$)