Question

Find the line parallel to the line y=3x+5 which passes through the point (1,4). a. y=-1/3x+1 b. y=-3x+1 c. y=1/3x+1 d. y=3x+1

Answer 1

D

Explanation:

We want to find the equation of the line parallel to y = 3x+5 and goes through the point (1,4).

First, since the new line is parallel, their slopes must be equivalent. Therefore, the slope of our new line must also be 3.

Since we know the slope and a point, we can consider the point-slope form:

`y-y_1=m(x-x_1)`

The slope m is 3. We can let the point (1,4) be x₁ and y₁. Thus:

`y-4=3(x-1)`

Distribute the right:

`y-4=3x-3`

Add 4 to both sides:

`y=3x+1`

And we're done!

The correct answer is D.