y is half of x plus 10

Answer 1

First look for the "is" or "equals" or the equivalent to see which terms go on either side of the equation.

"Half of x plus 10" can be expressed by (x/2) +10 or (x + 10)/2, it's not clear.

So equation is either y = (x/2) + 10 or y = (x + 10)/2.

Both are straight lines with positive slope of 1/2, but the former has a y-int of 10 and the latter has a y-int of 5.

Answer 2

To solve this, you must presume the writer of the phrase understands the English equivalents of PEMDAS (order of operations).

If the author of the phrase meant (1/2) × ( x+ 10), the phrasing should have been:

"half of THE SUM of x + 10"

[capitalization added for emphasis only]

or

"half of THE RESULT of x + 10"

or something similar to indicate that x + 10 should be completed before being divided by 2.

Since such bracketing words were not included in the phrase, you can presume that the correct interpretation is (x/2) + 10. PEMDAS requires you to divide (or multiply) before adding.

Also, since there is no wording to indicate this is an equation, such as

"y is ...", "f(x) is defined to be", or something similar before (or after) the phrase "one half of x+ 10", there is no justification to presume this is an equation. It looks like the right-hand side of a linear equation, but it may be just an expression.

Teachers often use sets of such phrases to help students learn how to "translate" word phrases into their mathematical equivalents.