Question

What do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular

Answer 1

Answer:

Option A: The same line

Explanations:

The slope-intercept form of the equation of a line can be written as:

y = mx + c

Where m is the slope

and c is the intercept

Let us express the two equations given in the slope-intercept form

For the first equation:

y - 3 = 2(x - 3)

y - 3 = 2x - 6

y = 2x - 6 + 3

y = 2x - 3

The slope, m = 2

The intercept, c = -3

For the second equation:

y + 5 = 2(x + 1)

y + 5 = 2x + 2

y = 2x + 2 - 5

y = 2x - 3

We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line