Question

What do the following two equations represent?

y-3=2(x-3)
y+5=2(x+1)
A The same line.
B Distinct parallel lines.
C Perpendicular lines.
D Intersecting, but not perpendicular lines

Answer 1

The equations y - 3 = 2(x - 3) and y + 5 = 2(x + 1) represent distinct parallel lines because they have the same slope but different y-intercepts.

Step-by-step explanation:

The two equations given are y - 3 = 2(x - 3) and y + 5 = 2(x + 1). To understand what these equations represent, it is important to look at the slope (m) of the lines and their y-intercepts (b). Both equations can be simplified to the slope-intercept form, which is y = mx + b.

For the first equation, y - 3 = 2(x - 3), simplifying gives us y = 2x - 3; thus, the slope (m) is 2, and the y-intercept (b) is -3. For the second equation, y + 5 = 2(x + 1), simplifying gives us y = 2x - 2; hence, it has the same slope of 2, but a different y-intercept of -2.

Since both lines have the same slope but different y-intercepts, they are distinct parallel lines. Therefore, the answer to the question is option B, Distinct parallel lines.