Question

The question is the picture thanks for helping

Answer 1

Answer:

Answer is option b)

Answer is given below with explanations.

Step-by-step explanation:

$a \: walking \: path \: is \: represented \: by \: \\ y = - 4x - 6 \\ 4x + y + 6 = 0 \\ given \: that \\ a \: new \: path \: will \: be \: built \: perpendicular \\ \: to \: \: the \: walking \: path \\ the \: equation \: of \: the \: line \: perpendicular \: to \\ 4x + y + 6 = 0 \: is \\ x - 4y + k = 0 \\ since \: it \: passes \: through \: ( - 4,10) \\ substitute \: x \: = - 4\: and \: y = 10 \: in \: required \: equation \\ - 4 - 4(10) + k = 0 \\ k = 44 \\ then \: the \: equation \: is \\ x - 4y + 44 = 0 \\ adding \: 4y \: on \: both \: sides \\ x + 44 = 4y \\ dividing \: by \: 4 \: on \: both \: sides \\ y = \frac{x}{4} + 11 \\ y = \frac{1}{4} x + 11 \\ so \: the \: answer \: is \: option \: b) \: \frac{1}{4} x + 11$

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Answer 2

Answer:

The answer is option B

Equation of a line is y = mx + c

Where

m = slope

From the equation y = - 4x - 6

Slope = - 4

Since the lines are perpendicular to each other the slope of the other line will be the negative inverse of the original line

That is

m = 1/4

Equation of the line using point ( - 4 , 10) is

y - 10 = 1/4(x + 4)

y - 10 = 1/4x + 1

y = 1/4x +1 + 10

y = 1/4x + 11

That's option B

Hope this helps