Question

1. does the equation represent a linear or nonlinear function? explain. 2x + 3y = 7

Explanation:

Step1: Rearrange to slope-intercept form

Subtract $2x$ from both sides:
$3y = -2x + 7$

Step2: Isolate $y$

Divide all terms by 3:
$y = -\frac{2}{3}x + \frac{7}{3}$

Step3: Check linear function criteria

The equation matches the linear form $y=mx+b$, where $m=-\frac{2}{3}$ (slope) and $b=\frac{7}{3}$ (y-intercept). All variables have an exponent of 1, no variable products or non-linear terms.

Answer:

This is a linear function. When rewritten in slope-intercept form $y = -\frac{2}{3}x + \frac{7}{3}$, it fits the standard linear function structure $y=mx+b$, with all variables raised to the first power and no non-linear operations present.