Graph and shade the inequality y< 4/5x+3

first off, let's  notice something, we are using < or less than, which means our line will be a dashed line, meaning it will not include points at the borderline, and after that, let's then graph the line for y = (4/5)x + 3, the EQUATion equivalent.

we'll do a true/false check on the regions of the line, to see which region gets shaded, namely which one is the "true" region.

well, let's try say hmmm point (0,0) where x = 0 and y = 0, let's check that

now hmmmm is 0 really less than 3? is that really true?  yeap, 0 is indeed smaller than 3, that means that the (0,0) point lies on the "true" region, and that's the one we'll shade.

Check the picture below.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1