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y = 4
x = 5
y = 7
x = 7
So this is actually much easier than it looks. A powerful assumption can be made right from the get-go. Notice that the problem states that the line is perpendicular to the line x=4. Recall that perpendicular lines form 90 degree angles with each other and have opposite slopes. The line x=4 is actually not a function, since on the line, there are infinite values of y that satisfy the point x=4. This makes its slope actually indeterminate. However, simply visualize what a line would look like if it formed a 90 degree angle with the line x=4. You should realize that the line formed is perfectly horizontal (since a horizontal line is the only kind of line that can form a right angle with a vertical line) and thus has some equation y = ?.
Now, to find what that value is. The problem also states that the line passes through the point (5,7). Visualize yet again the graph of y = ?. Yes, I know that there's no value for y, but any graph of y = (number) means that there's a horizontal line passing through the point (0, (number)). This means that for any line y = ?, x varies infinitely but y stays constant, at some value. But if the line passes through (5, 7), then you know that the value of y that the line passes through is 7. That should give you the value that the y-line is constantly equal to.
For this one, keep in mind what you learned in the last problem. Since y = -2, Then regardless of what value x takes on, y is ALWAYS equal to -2. So you can already eliminate three of the choices and see which answer is correct. For any line y=?, y does not change with respect to x. x can be whatever it wants and y will always stay the same.
For example, if I had the line y=6, y will always be equal to 6 for any value of x. If x = 6, y = 6. If x = 1, y = 6. If x = -252491, y is still equal to 6.