So far you have mostly worked with equations. there are special types of equations, called functions, that have exactly one output for every possible input into the equation. an example of this in the real world is the amount of money you are charged at a store: the input is the item you are purchasing, and the output is the money you are charged. individual items have one price, so this is an example of a function. can you think of any other examples of functions? why might this type of equation be useful?

Can you think of any other examples of functions?

Yes! Like putting a check in the bank, that is the input- and then the money you take is the output. You can even use food to compare input and output! Ingredients are the input, and the final dish/dessert is the output. If you wanted something more mathematical, you can use a graph to find the input and output. If you know a few points, you can create a whole line of x and y points, where x= input and y=output. You can also consider getting gas for your car, the money is the input, and the gas (in return) is the output. <== these are just a few examples. 

Why might this type of equation be useful? 

When you are trying to find the points for a line or looking for the unit price for something, functions can be very useful! You can find what y would be when x equals 1, 2, 3, 4, etc. I know I use this all the time! For example, trying to find the best price for something in the grocery store. There are a lot of options, and if you find the unit price with functions, it makes it easier to get the best deal.

I hope this helps!
~kaikers

The first one is 2/3the second is 1/160the third is 4/125

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .