graph a relation ship in which the value of y is 5 less than half the value of x

Question

I know the answer is y=0.5x+3 but I would like to know why it is that answer

Answer 1

Not sure you know how the answer is y = (1./2)x + 3? Was this a multiple choice question? The answer is actually y = (1/2)x - 5.

y IS 5 less than the value of 1/2 x. So for example if x = 20, 1/2 (20) = 10, and 5 less than 10 is 10 - 5 = 5.

Another example: x = 40, 1/2 (40) = 20, and 5 less than 20 is 15.

This is an example of translating word phrases into Algebra. "y IS" translates into "y = ". You can find 1/2 the value of x by multiplying 1/2 times x (or divide x by 2). You can also use a decimal as you suggested (0.5x). Five less than that value is found by subtracting 5.

To graph the relationship you want to realize that this is the equation of a line with a slope of 1/2 and a y-intercept located at (0,-5).

Here is a Desmos graph illustrating the above. Notice in the table that the y value "f(x)" is always 5 less than 1/2 the x value. Add some more rows to the table by inserting new values for x.

desmos.com/calculator/dgkqzsn8p1