Question

What is the equation of a line parallel to y = 2x + 3 and passes through the point (4, 1)?

Group of answer choices

y = 2x - 7

y = 2x + 9

y= 2x + 2

y = 1/2x - 1

Answer 1

y = 2x - 7 (first choice)

Explanation:

Equation of a line in slope-intercept form is

y = mx + b where m = slope and b = y-intercept

Parallel lines have the same slop
Line y = 2x + 3 has slope 2

So the parallel line has also slope 2 and is of the form y = 2x + b

To find b, sub for y and x using the given point:

1 = 2(4) + b

⇒ 1 = 8 + b

Subtract 8 from both sides
1 - 8 = 8 - 8 + b

- 7 = b

rewritten as b = -7

So equation of line is y = 2x - 7