Which of the following lines are perpendicular to the line y=-1/4x+6

(you may choose more than one answer)
4x-y=2
y=4x
4x+y=6
1/4x-y=6
-4x+y=3

the slope must be

1/(-1/4)
which means m = +4
the first one is a yea y = +4 x - 2
the second one is a yes y = +4 x + 0
the third one is a no y = (1/4) x - 6
the fourth one is a yes y =+4 x + 3
Please check your reply Lady P

Wow... it has been 6 years.

4x+y=6 is a for sure answer. I think -4x+y=3 might be the second answer Im not sure though.

There should be three answers:) Thanks for your help LadyPhantomhive

Seven years

To determine which lines are perpendicular to the line y = -1/4x + 6, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line is in slope-intercept form (y = mx + b), where the coefficient of x is the slope. In this case, the slope of the given line is -1/4.

To find the negative reciprocal of -1/4, we take its reciprocal (flipping the fraction) and negate it (change the sign). So, the negative reciprocal of -1/4 is 4.

Now, we can compare the slopes of the answer choices to determine which lines are perpendicular.

1. 4x - y = 2:
To put this equation in slope-intercept form, we can rearrange it to y = 4x - 2. The slope of this line is 4, which matches the negative reciprocal of the given line's slope. Therefore, this line is perpendicular.

2. y = 4x:
This line already has a slope of 4, which is the negative reciprocal of the given line's slope. Hence, this line is perpendicular.

3. 4x + y = 6:
By rearranging this equation, we can write it as y = -4x + 6. The slope of this line is -4, which is not the negative reciprocal of the given line's slope. Hence, this line is not perpendicular.

4. 1/4x - y = 6:
Rearranging this equation to slope-intercept form, we get y = 1/4x - 6. The slope of this line is 1/4, which is not the negative reciprocal of the given line's slope. Therefore, this line is not perpendicular.

5. -4x + y = 3:
Rewriting this equation in slope-intercept form, we obtain y = 4x + 3. The slope of this line is 4, which is not the negative reciprocal of the given line's slope. Consequently, this line is not perpendicular.

Based on the analysis, the lines that are perpendicular to y = -1/4x + 6 are:
- 4x - y = 2
- y = 4x

I mean -1/(-1/4) = +4