Explain how you know. Is the point (20,24) on line ℓ? Explain how you know. Is the point (80,100) on line ℓ? Explain how you know.

Answer/Step-by-step explanation:

First find the equation of the line. The graph is a proportional graph. Hence, the equation would be in the form is y = kx.

Where k I stye constant of proportionality (y/x).

Using a point on the line, (4, 5),

k = y/x = ⁵/4

Substitute ⁵/4 into y = kx.

Thus, the equation of the graph would be:

y = ⁵/4x

Plug in the value of the x and y coordinates of a point into the equation to determine if the point is on line l. If it makes the equation true, then it is a point on the line.

Thus:

✍️For the point, (20, 24), substitute x = 20, y = 24 in y = ⁵/4x

24 = ⁵/4(20)

24 = 5(5)

24 = 25 (NOT TRUE)

✅Therefore, the point, (20, 24) is not a point on line l.

✍️For the point, (80, 100), substitute x = 80, y = 100 in y = ⁵/4x

100 = ⁵/4(80)

100 = 5(20)

100 = 100 (TRUE)

✅Therefore, the point, (80, 100) IS A POINT on line l.

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

step-by-step explanation:

is their an equation anywhere i can take a   look at it and see if i am right.