None of those equations are perpendicular to y = x + 5.
One way to write the equation for a line graph is called y-intercept form which is written as:
y = mx + b
where 'm' is the slope and 'b' is where the graph crosses the y axis.
The equation given was:
y = x + 5 or equivalently
y = (1 * x) + 5 since 1 times any number gives us the number itself 1 * x = x always.
This means that the slope of the line is 1 or equivalently 1/1 if it is easier to think about the slope as "rise over run".
And that the y intercept is 5.
When dealing with parallel or perpendicular lines, you are mostly focused on the slope, the y intercept does not matter in this case.
If the line we were looking for were parallel we would want the slope to be the same which would be 1. Since the slope we want should be perpendicular we want the negative inverse. This means we take the slope, multiply it by negative one, and flip the fraction. Here are a few ways to think about the negative inverse symbolically: f(m) = -1/m
(you can think about "f(m)" as something you do to the slope 'm' in order to find the perpendicular slope)
So! The perpendicular slope in this case would be:
f(1) = -1/1
or just plain -1.
This means we are looking for an equation with a slope of -1.
y = 1/2 * x - 5 has a slope of 1/2
(also be carful of how you type these equations. Technically 1/2x implies 1 / (2x) where x is in the denominator. It would be better to write (1/2)x - 5)
y = (-1/2)x - 5 has a slope of -1/2
y = 2x + 10 has a slope of 2
y = -2x + 10 has a slope of -2
None of these numbers are the one you want. There are a few possibilities:
Part of this problem was finding the equation to a line where you found y = x + 5, but this was not the intended equation to find.
The answer is intentionally "none of the above"
Someone along the way made a mistake and forgot to include a correct answer.
Let me know what happened! I really don't like it when teachers ask confusing misleading questions.