Janelle is planning a party. The cost for 20 people is $290. The cost for 45 people is $590. Write the equation in slope intercept form to represent the cost y of having a party for x people.

Answer: y = 12x + 50

Step-by-step explanation:

Let y represent the cost of having the party.

Let x represent the number of people who would attend the party.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 - x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given

y2 = 590

y1 = 290

x2 = 45

x1 = 20

Slope, m = (590 - 290) / (45 - 20) = 300/25 = 12

To determine the intercept, we would substitute x = 20, y = 290 and m = 12 into y = mx + c. It becomes

290 = 12 * 20 + c = 240 + c

c = 290 - 240 = 50

The equation becomes

y = 12x + 50