Question

The coordinates below represent two linear equations.

Answer 1

The answer is d infinitely many

Answer 2

First write the equations in the slope-intercept form:
$y=mx+b \\ \\ m=\frac{y_2-y_1}{x_2-x_1}$

Line 1 passes through the points (-6,-6) and (-4,-3).
$m=\frac{-3-(-6)}{-4-(-6)}=\frac{-3+6}{-4+6}=\frac{3}{2} \\ \\ (-6,-6) \to x=-6, \ y=-6 \\ -6=\frac{3}{2} \times (-6) + b \\ -6=-9+b \\ b=3 \\ \\ y=\frac{3}{2}x+3$

Line 2 passes through the points (0,3) and (2,6).
$m=\frac{6-3}{2-0}=\frac{3}{2} \\ \\ (0,3) \to x=0, \ y=3 \\ 3=\frac{3}{2} \times 0 + b \\ b=3 \\ \\ y=\frac{3}{2}x+3$

These are two identical lines so the system of equations has infinitely many solutions. The answer is D.