Question

alejandra correctly wrote the equation $y - 3 = \frac{1}{5}(x - 10)$ to represent a line that her teacher sketched. the teacher then changed the line so it had a slope of 2, but still went through the same point. which equation should alejandra write to represent the new line?\
\\(\circ\\) $y - 6 = 2(x - 10)$\
\\(\circ\\) $y - 2 = \frac{1}{5}(x - 10)$\
\\(\circ\\) $y - 3 = \frac{1}{5}(x - 2)$\
\\(\circ\\) $y - 3 = 2(x - 10)$

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 from the original equation

In the original equation $y - 3=\frac{1}{5}(x - 10)$, by comparing with the point - slope form $y - y_1=m(x - x_1)$, we can see that the point $(x_1,y_1)$ is $(10,3)$ and the slope $m=\frac{1}{5}$.

Step3: Determine the new equation

The new line has the same point $(10,3)$ and a slope $m = 2$. Using the point - slope form $y - y_1=m(x - x_1)$ with $x_1 = 10$, $y_1=3$ and $m = 2$, we substitute these values into the formula:
$y-3 = 2(x - 10)$

Answer:

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