Aline goes through the point (6,–2) and has a slope of –3. what is the value of a if the point (a,7) lies on the line?

The value of a in the point (a, 7) is 3

The slope intercept equation is as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

Let's find b using (6, -2)

m = -3

y = -3x + b

-2 = -3(6) + b

-2  = -18 + b

b = -2 + 18

b = 16

Therefore,

y = -3x + 16

let's find the value of a in (a, 7)

7 = -3x + 16

7 - 16 = -3x

-9 = -3x

x = -9 / -3

x = 3

Therefore,

a = 3

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question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.