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? y – 6 = 2(x – 10) y – 2 = (x – 10) y – 3 = (x – 2) y – 3 = 2(x – 10)

Answer 1

the last one would be the correct answer y - 3 = 2(x - 10)

Answer 2

Option D is correct

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

Explanation:

Using point slope form:

The equation of line is given by:

`y-y_1=m(x-x_1)` .....[1] where m, is the slope and
`(x_1, y_1)` is the point on the line

As per the statement:

Alejandra correctly wrote the equation y – 3 = (x – 10) to represent a line that her teacher sketched.

The line passes through the point i.,e (10, 3)

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

⇒ slope(m) = 2

Substitute these in [1] we have;

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

Therefore, an equation should Alejandra write to represent the new line is,

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