Write the equation in function form: y-x=1

Question

I really need help on this and a few more problems- Write the equation in function form: 5x-2y=6

Identify the domain and the range: (1,2) (-2, 4) (3, 5) (-1, 9) Is this a function?

Identify the domain and the range (-1, 3) (-1, 0) (2, 4) (3, 5) Is this a function?

Graph: 2x - y = -4

Graph: y = 1/2x + 3

Identify the slope and the y intercept: 2x - 5y = 10

Identify the slope and the y intercept: x - 2y = 6

What is the slope: y = 2

I am really struggling with slope!!

Answer 1

Given a Linear equation, to put it into function form, just solve for y, that is, get everything on the right side of the equation except y.  This is easily done. The result can be called y = mx + b, a.k.a. slope intercept form. Surely this will be familiar to you and if not, review your textbook or equivalent material. (If you're being subjected to poorly designed Common Core stuff, I suggest that you use the internet & Youtube for review of topics such as Linear functions, Point slope form, Slope intercept form, etc.)

 

To graph, fill out this table:  when x = 0, y=____; when y=0, x=_____. This gives you two ordered pairs, and they're the y intercept and the x intercept, respectively.  (y intercept is the b of y=mx+b)  Plotting those two points enables you to draw the correct line (this always works unless b=0).

 

Identify the domain and range: (1,2) (-2, 4) (3, 5) (-1, 9) Is this a function? YES...since all the x value are unique.
Identify the domain and the range (-1, 3) (-1, 0) (2, 4) (3, 5) Is this a function? NO...since when x=-1, there are two different y values, so the graph violates the vertical line test & cannot be a function.

 

The domain is always the set of all listed x values; the range is always the set of all listed y values.