Find the equation of the line perpendicular to  y=−2 that passes through the point (4,  −2).

Step-by-step explanation:

the line

is a horizontal line on the -2 of the y-axis (for any x value, the y value is always -2).

Thus since is a horizontal line, a perpendicular line to a horizontal line has to be a vertical line.

Now, we want this vertical to pass through the point:

.

This means that the only option we have is the line:

because this is the equation of a vertical line sitting on the x = 4.

This can be better visualized in the attached image. where the red line is and the dotted blue line is

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.