Show that the equation y -2= 4(3x+5) is a liner and then tell if it represents a proportional or nonproportional relationship between x and y

y=12x+22 is linear but not proportional

Step-by-step explanation:

This is a linear equation because it has an x and y within the expression without exponents or other complex operators. We can rearrange and simplify the equation into slope-intercept form.

This linear equation follows the form y=mx+b where m is the slope and b is the y-intercept. For this function, m=12 and b=22. This is not a proportional relationship because the function's y-intercept is something other than 0.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: