Alejandra correctly wrote the equation y – 3 = y minus 3 equals StartFraction 1 Over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.(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?

The equation Alejandra should write to represent the new line should be

y-3 = 2(x-10)

Step-by-step explanation:

The equation Alejandra wrote for the line her teacher sketched is

y-3 = 1/5 (x-10).

This can be related to the equation of a line in point slope form. The equation of line in point slope form

is

y - y₁ = m (x - x₁)

Where (x₁, y₁) is a point on line

and m is the slope of the line.

Hence, for the equation Alejandra wrote

The line went through point (3,10) and the slope of the line is 1/5.

Now, from the question

The teacher changed the line so it had a slope of 2, but still went through the same point. That is, the line still went through point (3,10).

In the new line the teacher sketched, the values of x₁ and y₁ remain the same but the value of the slope (m) has changed.

The slope of the new line is 2, that is, m =2.

Therefore,

The equation that represents the new line is

y-3 = 2(x-10)

Hence, the equation Alejandra should write to represent the new line should be y-3 = 2(x-10).