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9 December, 11:14

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.

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  1. 9 December, 12:09
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    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
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