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

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?\n$y - 6 = 2(x - 10)$\n$y - 2=\frac{1}{5}(x - 10)$\n$y - 3=\frac{1}{5}(x - 2)$\n$y - 3 = 2(x - 10)$

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?\n$y - 6 = 2(x - 10)$\n$y - 2=\frac{1}{5}(x - 10)$\n$y - 3=\frac{1}{5}(x - 2)$\n$y - 3 = 2(x - 10)$

Answer

Explanation:

Step1: Identify the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. The original line is $y - 3=\frac{1}{5}(x - 10)$, so the point on the line is $(10,3)$.

Step2: Find the new equation

The new line has a slope $m = 2$ and passes through the point $(10,3)$. Substituting $m = 2$, $x_1=10$ and $y_1 = 3$ into the point - slope form $y - y_1=m(x - x_1)$, we get $y - 3=2(x - 10)$.

Answer:

D. $y - 3=2(x - 10)$