Question

What’s the equation of the line that be that passes through (4,2) and is parallel to the line y=2x-1

A) x-y=6
B) 2x-y=6
C) 2x-y=1
D) 2x-y=-1

Answer 1

y=mx+b

because the y=2x-1, so m=2

because we know (4.2), so we can bring it in to the function:

2=2x4+b

2=8+b

b=-6

So the other one is: y=2x-6

in other way it's 2x-y=6

Which means the answer is B.

Answer 2

This equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Note that parallel lines have the same slope.

The equation is y = 2x - 1; the slope is 2 and the y-intercept is (0, -1).

For our line parallel to the given line, we have y = 2x + b, as the slopes are the same. To find b (the y-intercept), plug the point on the line - (4, 2) - for x and y in the equation and solve algebraically for b.

y = 2x + b

2 = 2(4) + b

2 = 8 + b

-6 = b

We can now complete our equation!

y = 2x - 6

However, notice how the options aren't in slope-intercept form. Simply isolate and negate the constant to figure out which one is correct.

y = 2x - 6

y - 2x = -6

-y + 2x = 6

2x - y = 6

Answer:

The equation of the line that passes through (4, 2) and is parallel to the line y = 2x - 1 is B) 2x - y = 6.