Question

Which equation represents a linear function?​

Answer 1

Answer:

$\large\boxed{D.\ y=\dfrac{1}{2}(x-3)-2x}$

Step-by-step explanation:

The equation of linear function in slope-intercept form:

$y=mx+b$

$A.\ y=x(2-3x)=2x-3x^2\qquad\text{NOT, because we have }\ x^2\\\\B.\ y=\dfrac{1}{2}x^2+3x-1\qquad\text{NOT, bacause we have }\ x^2\\\\C.\ y=\dfrac{1}{2}x(2x-1)+3=x^2-\dfrac{1}{2}x+3\qquad\text{NOT, because we have}\ x^2\\\\D.\ y=\dfrac{1}{2}(x-3)-2x=\dfrac{1}{2}x-\dfrac{3}{2}-2x=-1\dfrac{1}{2}x-\dfrac{3}{2}\qquad\boxed{\bold{YES}}$