Question

Which of the following equations describes the line passing through (3, -1) and parallel to the line described by y = 2x + 0?

A) y = 2x - 7
B) y = 2x + 5
C) y = 2x - 1
D) y = 2x + 3

Answer 1

The equation of the line that is parallel to y = 2x and passes through the point (3, -1) has the same slope, which is 2. Using the point-slope form, the equation is found to be y = 2x - 7.

Step-by-step explanation:

The question asks for the equation of a line that passes through a given point (3, -1) and is parallel to another line given by y = 2x + 0. To answer this, we first recognize that parallel lines have the same slope. The original line has a slope of 2, so the line we are looking for must also have a slope of 2.

Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, we can plug in our values:

• m (slope) = 2
• (x1, y1) = (3, -1)

So, y - (-1) = 2(x - 3). Simplifying, we get:

y + 1 = 2x - 6

Then, subtracting 1 from both sides to get y by itself:

y = 2x - 7

Therefore, the equation for the line we are looking for is y = 2x - 7, which corresponds to option A).