Answer:
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).
