Question

What is the equation of the line that passes through the point (4, 6) and is parallel to the line 2y - 4x = 1?

Select one:
O A. y = - 2x - 2
O B. y = 2x + 2
O C. y = x - 2
O D. y = 2x - 2

Answer 1

D. y = 2x - 2

Explanation:

1) First, find the slope of the given line. Place it in slope-intercept form to identify its slope easily. Isolate the y in the equation:

`2y-4x = 1\\2y = 4x+1\\y = 2x+(1)/(2)`

A line placed in slope-intercept form is represented by the formula
`y = mx + b`. The
`m`, or the coefficient of the x-term, represents the slope. Thus, the slope of this line is 2.

2) Lines that are parallel share the same slope. So, the slope of the parallel line will have 2 as its slope as well.

We now have enough information to write the equation of the line in point-slope form. From there, we can convert it to slope-intercept form and find out which option is correct.

Use the point-slope formula
`y-y_1 = m (x-x_1)` and substitute values for
`m`,
`x_1`, and
`y_1`. Since
`m` represents the slope of the line, substitute 2 in its place. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, substitute the x and y values of (4,6) into the formula as well. Then, with the resulting equation, isolate y like before to find which option is correct:

`y-6 = 2(x-4)\\y-6 = 2x-8\\y = 2x-2`

So, option D is correct.