What is the y-intercept of the line perpendicular to the line...
.that includes the point (3, 1)?

A)
B)
C)
D)

D) 5

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes.

The line: has a slope of as it is  in y=mx+b form, where m is the slope, and b is the y-intercept.

Since the slope is , we see that the negative reciprocal slope is , as is the reciprocal (flip the numerator and denominator).

From here, we can use point slope form: , where is  the point. In this case, (3, 1) is the point.

Thus, we have: as our final equation.

Simplifying:

And: , which gives us the y-intercept to be 5.

Let me know if this helps!

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!