Question

Which of the following is the equation of a line parallel to 3y = 6x + 5 that passes through (3, 3)? A. y = 2x - 1 B. y = 2x - 3 C. y + 2x = 1 D. y + 3 = 6x​

Answer 1

B) y = 2x - 3

Explanation:

3y = 6x + 5 To put in the slope intercept form. Divide all the way through by 3

y = 2x + 5/3

When lines are parallel, they have the same slope.

So the slope will be 2. We will use the point to find the y intercept

m = 2

x = 3 This is from the point (3,3)

y = 3 this is from the point (3,3)

y = mx + b

3 = 2(3) + b

3 = 6 + b Subtract 6 from both sides

3-6 = 6- 6 + b

-3 = b

Now that we have the slope (2) and the y intercept (-3) we can write the equation.

y = mx + b

y = 2x -3

Answer 2

First, we should find the slope of the line we're starting with.

3y = 6x + 5 can be put into slope-intercept form by dividing both sides by 3.

y = 2x + 5/3

The slope of this line is 2.

A parallel line has to have a slope of 2 as well, so we know we're looking for a line with a slope of 2.

Options A and B have that. Options C and D do not.

Now if (3,3) is a point on the line, then (3,3) must also be a solution for the equation.

Checking Option A:

3 = 2(3) - 1 is not true. 3 ≠ 6 - 1

Checking Option B:

3 = 2(3) - 3 is true. 3 = 6 - 3

Option B is the answer, since it has the right slope and works for the point (3,3).