Question

I need help with #1 and 2 please I’m struggling

Answer 1

The slope of a line perpendicular to other line is the negative reciprocal of the slope.

This means, if the slope of a line is x, the slope of a perpendicular line will be:

`-(1)/(x)`

Then , the first thing we should do is to find the slope of f(x).

To find the slope of a line that passes two points P and Q we use:

`\begin{gathered} \begin{cases}P=(x_p,y_p) \\ Q=(x_q,y_q)\end{cases} \\ \text{slope}=(y_p-y_q)/(x_p-x_q) \end{gathered}`

In this case, we can use P = (1, 4) and Q = (-3, 2)

Then:

`\text{slope}=(4-2)/(1-(-3))=(2)/(4)=(1)/(2)`

Now, we know that the slope of g(x) is perpendicular to f(x) which has a slope of 1/2

The reciprocal is:

`(1)/(2)\Rightarrow(2)/(1)=2`

And to make it the negative, we multiply by (-1):

`2\cdot(-1)=-2`

Thus, g(x) has a slope equal to -2