Final answer:
None of the points (1,5), (2,10), (3,7), or (4,14) match the y-values calculated by the equation y=1/2 x-5 when their x-values are plugged in, hence they are not solutions to the equation.
Step-by-step explanation:
To determine which points are solutions to the equation y=1/2 x-5, we must plug in the x-values from each point into the equation and see if the resulting y-value matches the y-value in the point given. The dependence of y on x indicates how y changes with respect to x. When x is 1, the equation yields y=1/2(1)-5, which simplifies to y=-4.5; this does not match the y-value in the point (1,5) provided.
Using the same process for the other points, none of them will satisfy the equation y=1/2 x-5, because the y-values calculated by plugging the x-values from the points into the equation will not match the y-values given in the points. Therefore, none of the points (1,5), (2,10), (3,7), or (4,14) are solutions to the equation y=1/2 x-5.