What is the equation of the line that has a y-intercept of 5 and is parallel to the line represented by the equation below?
2x - y = 16
A. y = 2x + 5
B. y = -2x + 5
C. y = 1/2x - 5
D. y = -1/2x - 5
I guessed B for this one, but another choice of mine was A. I'm not sure which one to pick.
However, the answer is (A)
Thank you, Steve
y = 2 x - 16 is original so slope = 2
y = 2 x + b
when x = 0, y = 5
so
y = 2 x + 5 which is A
To find the equation of a line that is parallel to a given line, we need to understand that parallel lines have the same slope. The given equation is 2x - y = 16. We need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Rearranging the equation 2x - y = 16, we add y to both sides:
2x - y + y = 16 + y
This simplifies to:
2x = y + 16
Next, to isolate y, we subtract 16 from both sides:
2x - 16 = y
Therefore, the slope-intercept form of the given equation is y = 2x - 16. Now we can determine the slope.
The slope of the given equation is the coefficient of x, which is 2. Since we want a line that is parallel to this equation, the slope will be the same in the new equation.
The y-intercept is given as 5 in the question. So, the equation of the line parallel to 2x - y = 16 with a y-intercept of 5 would be y = 2x + 5.
Therefore, the correct answer is A. y = 2x + 5.