Question

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

Answer 1

y=12x+22 is linear but not proportional

Explanation:

`y-2=4(3x+5)`

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.

`y-2=4(3x+5)\\y-2=12x+20\\y-2+2=12x+20+2\\y=12x+22`

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.