Final answer:
The equation 6-2/5x= 3y + 8x is linear because it can be rearranged to the standard linear form y = mx + b, with a slope m = -\(\frac{38}{15}\) and y-intercept b = 2.
Step-by-step explanation:
To determine whether the equation 6-2/5x = 3y + 8x represents a linear or nonlinear equation, we need to see if it can be written in the form y = mx + b, where m is the slope and b is the y-intercept. If it can, then the equation is linear. Let's attempt to rearrange the equation to this form:
First, we group the terms involving y on one side and the terms involving x on the other:
3y = -8x +2/5x + 6
Next, we simplify the x terms on the right-hand side:
3y = -40/5x + + 6
3y = -\(\frac{38}{5}x\) + 6
By dividing every term by 3 to solve for y, we get:
y = -(38/5x)/(1/3) + 2
Or
y = -38/15x+ 2
Since we now have the equation in the form y = mx + b, with m as -\(\frac{38}{15}\) and b as 2, it is clear that the equation represents a linear relationship.