8th Grade Math Question of the Day

1. $y=-2x+7$
2. $y=\dfrac{1}{2}x-4$
3. $y=x^2$ (correct answer)
4. $y=9x$

Explanation: This question tests interpreting y=mx+b as defining a linear function with a straight-line graph and constant slope m, while identifying non-linear functions with curved graphs or non-constant rates, such as those with x squared, in denominators, absolute values, or exponents. Linear functions like y=mx+b have constant slope m (y changes by m per unit x) and y-intercept b, graphing straight through (0,b); non-linear ones vary, e.g., y=x² is a parabola with increasing slope (points (1,1),(2,4),(3,9) show y-differences 3,5—not constant), y=1/x hyperbola, y=|x| V-shape with slope shift. For instance, y=3x+2 is linear with constant rate 3 and straight graph, but y=x² curves with points not collinear, demonstrating variable rate (slope between (0,0)-(1,1) is 1, but (1,1)-(2,4) is 3). The non-linear function here is C, y=x², lacking constant rate and straight graph, while A, B, D are linear in y=mx+b form. Common errors include calling y=x² linear because it has x (ignoring exponent 2 causing curvature) or misinterpreting m and b in linear ones, like swapping slope and intercept. Identifying linear: (1) rewrite as y=mx+b, (2) check x exponent=1, (3) graph for straightness, (4) confirm constant slope via points. Interpreting: m is rate/steepness, b starting value; mistakes: assuming all variable equations are linear or claiming curved graphs have constant rates.