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
, where
and
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 = 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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