the price, p , for different size orders of custom posters of the swim team picture, n , is the given table.

number of posters ordered and the prices// 1= $70 5=$150 20=$450 50=$1050

can a linear equation be used to model the situation? if it can, what is the slope and the y-intercept of the equation?

a) linear: slope 30, y-intercept= 0

b) linear: slope 20, y-intercept= 50

c) linear: slope 20, y-intercept= 0

d) a linear equation cannot be used

you have the points
(1,70)
(5,150)
(20,450)
(50,1050)

can this be linear?
calculate theoretical m:
with (5,150), (20,450)
(450-150)/(20-15)=300/15=20

y=mx+b
if we insert (5,150):
150=20*5+b
50=b

does this match (1,70)?
70=20*1+50?yes
(5,150), (20,450)? yes, because we used them to calculate it

(50,1050)?
1050=50*20+50? yes

therefore, yes it can be modeled with y=20x+50
so answer b) linear: slope 20, y-intercept= 50 is correct

kapoorprachi783 kapoorprachi783 · Answer 2 · 2022-05-25T21:57:17+02:00

The correct answer is option b) linear: slope 20, y-intercept= 50

How to solve the y-intercept of the equation?

To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

When n = 1, p = 70

n = 5, p = 150

Using y = mx + c where y = p and x = n

m = slope

c = y-intercept

Therefore,

⇒ 70= m(1) + c

⇒ 70=m+c ..... (1)

and,

⇒ 150= m(5)+c

⇒ 150 = 5m + c ..... (2)

Subtracting equation (1) from (2),

⇒ 150 = 5m + c - 70 = m+c

⇒ 80 = 4m + 0

⇒ 4m = 80

⇒ m = 80 / 20

Therefore, the slope is 20

To find the y-intercept

Substitute 20 for m in equation 1.

⇒ 70 = m + c

⇒ C = 70 - m

⇒ 70-20 = 50

y-intercept = 50.

The y-intercept formula says that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it.

Learn more about the y-intercept of the equation here: brainly.com/question/1884491

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