The graph shows a line and two similar triangles. On a coordinate plane, a line goes through (0, 0) and (6, 10). A small triangle has a rise of 5 and run of 3, and a larger triangle has a rise of 10 and run of 6. What is the equation of the line? y = 5 x y = 3 x y = three-fifths x y = five-thirds x

The value of the equation for y is five third of the x. Thus the option 4 is correct.

Given-

The points through which line passes (0, 0) and (6, 10).

The equation of the line

As we know the two points are (0, 0) and (6, 10).

Slope of the line,

Standard equation of the line is,

Substitute the value of m and point (0,0)

Hence, The value of the equation for y is five third of the x. Thus the option 4 is correct.

For more about the equation of line follow the link below-

link

y = (5/3)x

y = five-thirds x

Step-by-step explanation:

Slope = 10/6 = 5/3

Y-intercept = 0

y = (5/3)x

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!