Question

A caterer charges $120 to cater a party for 15 people and $200 for 25 people.

Answer 1

The equation in slope-intercept form for this function is y = 8 x

The slope represents the unit cost

A party for 40 people would cost $320

Step-by-step explanation:

The linear equation in the form of slope-intercept is:

y = mx + b, where m is the slope of the line and b is the y-intercept

• $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line
• To find b substitute x and y of the equation by the coordinates of any point on the line

A caterer charges $120 to cater a party for 15 people and $200 for

25 people.

Assume that the cost, y, is a linear function of the number of people x

We need to write an equation in slope-intercept form for this function

We need to explain that the slope represent what

We need to find how much a party for 40 people would cost

∵ The slope-intercept form of the equation is y = mx + c

∵ y is the cost and x is the number of people

∴ x = 15 and y = 120 is a point on the line

∴ x = 25 and y = 200 is another point on the line

- Now we can use them to find the slope of the line

∵ $m=\frac{200-120}{25-15}=\frac{80}{10}$

∴ m = 8

∴ y = 8 x + b

- To find b substitute x by 15 and y by 120 in the equation

∴ 120 = 8(15) + b

∴ 120 = 120 + b

- Subtract 120 from both sides

∴ b = 0

∴ y = 8 x

The equation in slope-intercept form for this function is y = 8 x

∵ The slope = change of y ÷ change of x

∴ The slope = cost ÷ number of people

∴ The slope represents the cost per person

The slope represents the unit cost

∵ There are 40 people

∴ x = 40

∵ The equation of the cost is y = 8 x

∴ y = 8 × 40

∴ y = 320

∴ The cost is $320

A party for 40 people would cost $320

Learn more:

You can learn more about the linear function in brainly.com/question/4152194

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