examine the graph below. select the solutions to the graph from the following points. select three that apply.

Options (1), (2), (3)

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Given line on the graph is passing through two points (-3, 0) and (0, 1).

Slope of this line will be,

m =

   =

   =

y-intercept of the line 'b' = 1

Equation of the line will be,

y =

If the points given in the options satisfy the equation, they will be the solution of the line.

Option (1),

For (3, 2),

2 =

2 = 2

True.

(3, 2) is the solution.

Option (2)

For (21, 8),

8 =

8 = 8

True.

(21, 8) is the solution.

Option(3)

For (-15, -4),

-4 =

-4 = -4

True.

(-15, -4) is the solution.

Option (4)

For (12, 9)

9 =

9 = 5

False

(12, 9) is not the solution.

Option (5)

For (-6, 1)

1 =

1 = -1

False

(-6, 1) is not the solution.

Therefore, Options (1), (2), (3) are the solutions.

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!