Use the coordinates of the labeled point to find the point-slope equation of the line

A. y + 1 = -2(x-2)

Step-by-step explanation:

point-slope equation is : y - y1 = m (x -x1)

remember m= slope value

the given point is (2, -1) therefore we can substitute the values in:

y + 1 = m(x -2)

now to make sure our answer is complete we will solve for the slope:

looking back at the graph, the y-intercept value is 3, therefore we have a point of (0,3) and (2, -1)

with any two points you can determine a slope.

y2 - y1 / x2 - x1

therefore :

-1 -3 / 2 - 0

-4 / 2 = -2

therefore our m value is -2

this makes the completed point-slope equation:

y + 1 = -2 (x - 2) or A

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!

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