Question

The slope of a line is –2 and its y-intercept is (0, 3). What is the equation of the line that is parallel to the first line and passes through (2, 2)? A. 2x + y = 6 B. y = –2x + 3 C.y=1/2x +6 D.y=-2x-6

Answer 1

D. y=-2x-6

Explanation:

First start with what we know....

y = -2x + 3 (Slope Intercept Form)

Because of this we can eliminate B.

Parallel means that the lines wouldn't be touching which means they should have the same slope and the only one with the same slope is D.

Answer 2

For this case we have that an equation of a line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cutoff point with the y axis

They give us the following information:

`m = -2\\b = 3`

Then the line is:

`y = -2x + 3`

They ask us to find a parallel line. By definition, if two lines are parallel then they have the same slope. Thus, the line sought is of the form:

`y = -2x + b`

We look for the cut point "b" substituting the point where the line passes:
`(2,2)`

`2 = -2 (2) + b\\2 = -4 + b\\2 + 4 = b\\b = 6`

Finally, the line is:

`y = -2x + 6\\y + 2x = 6`

Answer:

Option A