Question

Type an equation for the line described. Type your answer in the form g(x)=mx+b. If a value is not an integer type it as a decimal rounded to the nearest hundredth. Do not put any spaces between your characters.A line perpendicular to h(x)=\frac{-1}{2}x+4 and passing through the point (-4,-1) The slope of our perpendicular line will be Answerand it has an equation of g(x)=Answer.

Answer 1

Slope of perpendicular line is: 2

If the line passes through the point (-4,-1), the equation will be:

y = 2x + 7

How to find the equation of the Line?

The general form of the equation of a line is:

y = mx + b

where:

m is slope

b is y-intercept

We are given an equation as:

h(x) = -¹/₂x + 4

Thus:

Slope = -¹/₂

A line perpendicular to it will have its' slope as the negative reciprocal.

Thus: Slope of perpendicular line is:

m = -1/(-¹/₂) = 2

If the line passes through the point (-4,-1), the equation will be:

(y - (-1)) = 2(x - (-4))

y + 1 = 2x + 8

y = 2x + 7

Answer 2

A line that is perpendicular to another has the inverse slope of the other times -1 . This can be written on the following equation:

`m1\text{ = }(-1)/(m2)`

If m2 is -1/2, thus:

`m1\text{ = }(-1)/(-(1)/(2))=2`

The next step is to apply the following equation of a line using the slope m1 and the point is given (-4,-1):

`y\text{ - yo = m1 (x-xo)}`
`y-(-1)\text{ = 2(x-(-4))}`
`y+1\text{ = }2x+8`
`g(x)=2x+7`

Obs: Consider 'y' as g(x).