Question

Any help? please make sure it's correct thank you

Answer 1

y = -
`(1)/(2)` x + 6

Explanation:

The slope will be perpendicular to equation through A and B because of the 90 degree angle at B.

Lines that are perpendicular have opposite reciprocal slopes.

The slope of the line we know is 2 (The slope is the number before the x). The opposite reciprocal is -
`(1)/(2)`.

Now that we have the slope we need a point on the line. They give us that point at (0,6) We will use the y value of 6 and the x value of 0 from the point given to find the y-intercept.

slope (m) = -
`(1)/(2)`

y = 6

x = 0

We will substitute all of this information into y = mx + b to solve for b (y-intercept)

y = mx + b

6 = -
`(1)/(2)` (0) + b

6 = b

Now that we have the slope (-
`(1)/(2)`) and the y-intercept (6) we can write the equation

y = -
`(1)/(2)` x + 6

Answer 2

y = -
`(1)/(2)` x + 6

Explanation:

the equation of a line in slope- intercept form is

y = mx + c m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

BC is perpendicular to AB

given a line with slope m then the slope of a line perpendicular to it is

`m_(BC)` = -
`(1)/(m)` = -
`(1)/(2)`

the line BC has point C at (0, 6 ) ⇒ c = 6

y = -
`(1)/(2)` x + 6 ← equation of line BC