Which equation represents a linear function? x = 3 y = \frac{16}{x} y = 3x^2 + 1 y = -3x + 10
The Correct Answer and Explanation is:
The equation that represents a linear function is:
✅ y = -3x + 10
Explanation
A linear function is a function that forms a straight line when graphed. It has the general form:y=mx+by = mx + by=mx+b
Where:
- yyy is the dependent variable,
- xxx is the independent variable,
- mmm is the slope of the line (rate of change), and
- bbb is the y-intercept (the value of yyy when x=0x = 0x=0).
Let’s analyze each option:
- x = 3
This is a vertical line, not a function. It does not pass the vertical line test (a vertical line intersects it at more than one point), so it’s not a function at all, let alone a linear one. - y=16xy = \frac{16}{x}y=x16
This is a rational function. It has a variable in the denominator and is not linear because its graph is a hyperbola, not a straight line. The rate of change is not constant. - y=3×2+1y = 3x^2 + 1y=3×2+1
This is a quadratic function because it includes an x2x^2×2 term. Its graph is a parabola, not a straight line. Therefore, it is not linear. - ✅ y=−3x+10y = -3x + 10y=−3x+10
This is a linear function. It matches the form y=mx+by = mx + by=mx+b, with:- Slope m=−3m = -3m=−3
- Y-intercept b=10b = 10b=10
Summary:
Among the given equations, only y=−3x+10y = -3x + 10y=−3x+10 is a linear function because it forms a straight line and has a constant rate of change. All other options fail to meet these criteria due to either having non-constant rates, non-linear terms, or not even being functions.
