Question

Alejandra correctly wrote the equation y – 3 = (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?

Answer 1

hello :
an equation should Alejandra write to represent the new line is :
y – 3 = 2 (x – 10)

Answer 2

The equation of new line is (y-3)=2(x-10).

Explanation:

If a line passing through the point (x₁,y₁) with slope m, then the point slope form of the line is

`(y-y_1)=m(x-x_1)`

It is given that Alejandra correctly wrote the equation

`(y-3)=(x-10)`

Here,

`m=1,x_1=10,y_1=3`

It means the slope of the line is 1 and the line passing through the point (10,3).

The teacher then changed the line so it had a slope of 2, but still went through the same point.

Now the slope of line is 2 and the line passing through the point (10,3). So the point slope form of the line is

`(y-3)=2(x-10)`

Therefore the equation of new line is (y-3)=2(x-10).