Question

Select the equation that is perpendicular to

y=6x-2 and has a y intercept at -6.



a
y=(1/6)x-6

b
y=(-1/6)x-6

c
y=(-1/6)x+6

d
y=6x-6

Answer 1

To find a line that is perpendicular to the line given by the equation \( y = 6x - 2 \) and has a y-intercept of -6, we first need to determine the slope of the given line.

The slope of the line \( y = 6x - 2 \) is 6. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line that is perpendicular to this will be:

\[
\text{slope} = -\frac{1}{6}
\]

Now we need to write the equation of a line with this slope and a y-intercept of -6. The equation of a line in slope-intercept form ( \( y = mx + b \) ) can be expressed as follows:

\[
y = -\frac{1}{6}x - 6
\]

Now, we can compare this with the options given:

a) \( y = \frac{1}{6}x - 6 \)

b) \( y = -\frac{1}{6}x - 6 \)

c) \( y = -\frac{1}{6}x + 6 \)

d) \( y = 6x - 6 \)

The correct choice, which has a slope of \( -\frac{1}{6} \) and a y-intercept of -6, is:

**b) \( y = -\frac{1}{6}x - 6 \)**.