Question

I need help with this, I've never really understood linear stuff.

Answer 1

OK; there's another answer but I haven't peeked.

y = -3 x + 7

A(4,-5): -3(4)+7=-12+7=-5 (4,-5) is on the line

B(4 ,19) . We got y=-5 when x=4 so this one isn't on the line.

C(1, 5) : -3(1)+7=4 not 5, not on the line

D(1, -19) : Still 4 not -19, not on the line

Answer: A

Answer 2

You have several possible points $(x,y)$. Any point that lies on the given line will have a $y$ value that you obtain by plugging in the corresponding value of $x$ into the equation of the line.

The line has equation $y=-3x+7$, so any point on the line will have the form $(x,-3x+7)$.

Among the four given points, there are only 2 different values of $x$ to check. We have

$x=4\implies y=-3(4)+7=-12+7=-5$

$x=1\implies y=-3(1)+7=-3+7=4$

which means the given line contains the points (4, -5) and (1, 4). So the answer is A.