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. Write anequation in slope-intercept form for this function. What does the slope represent?How much would a party for 40 people cost?

The equation in slope-intercept form for this function is y = 8 xThe slope represents the unit costA party for 40 people would cost $320Step-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[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the lineTo find b substitute x and y of the equation by the coordinates of any point on the lineA 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 xWe need to write an equation in slope-intercept form for this functionWe need to explain that the slope represent whatWe 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∵ [tex]m=\frac{200-120}{25-15}=\frac{80}{10}[/tex]∴ 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 xThe 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 personThe 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 $320A party for 40 people would cost $320Learn more:You can learn more about the linear function in brainly.com/question/4152194#LearnwithBrainly