Question

A caterer charges $275 for 15 people and $425 for 25 people. The cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this situation. *

Answer 1

The equation of the given situation is y = 15x + 50

Explanation:

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ A caterer charges $275 for 15 people

∵ A caterer charges $425 for 25 people

∵ x represents the number of people

∵ y represents the cost

∴ (x1, y1) = (15, 275)

∴ (x2, y2) = (25, 425)

→ Substitute them in the rule of the slope above to find it

∵ m =
`(425-275)/(25-15)=(150)/(10)`

∴ m = 15

→ Substitute it in the form of the equation above

∴ y = 15x + b

→ To find b substitute x by 15 and y by 275

∵ 275 = 15(15) + b

∴ 275 = 225 + b

→ Subtract 225 from both sides

∴ 275 - 225 = 225 - 225 + b

∴ 50 = b

→ Substitute it in the equation

∴ y = 15x + 50

∴ The equation of the given situation is y = 15x + 50