If a = {(x, y)|x + 2y = 7}, is set a a function?

Yes it is a function

Here are some reasons why

We can solve x+2y = 7 for y to get y = -0.5x+3.5; this equation is in slope intercept form y = mx+b. All equations in the form y = mx+b are linear and also a function.For any input x, there is exactly only one y value that pairs with it.The vertical line test can be used to effectively verify item #2 above. The idea is that it is impossible to draw a vertical line through more than one point on the graph. So it is said to pass the vertical line test.

The correct answer would be the fourth choice