Find an equation in slope-intercept form (where possible) for the line with y-in

Question

Find an equation in slope-intercept form (where possible) for the line with y-intercept - 2 and perpendicular to x + 8y = -9. The information in the chart gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24800) and (3, 26600) Find all values x = a where the function is discontinuous. Find the average rate of change for the function over the given interval. y = x2 + 7x between x = 1 and x = 9 If f(x) = -1/x and g(x) = determine the values of f g(3) and g f(3) If f(x) = 1/x + 1, then the expression f(1 + h) - f(1)/h can be simplified to

Explanation / Answer

4.slope intercept form :y=mx+c

x+8y=-9

As the line is perdicular to the above line

m*(-1/8)=-1

m=8

c=-2

so y=8x-2

b.

5).We need to find the equation which satisfies these two points

(1,24800),(3,26600)

slope =1800/2=900

y=900x+c

Put (1,24800)

24800=900+c

c=23900

y=900x+23900

d.

6.Just put the values of limits of the functions f(x)and g(x) to get the value of the limit of the desired function,

Desired result=(27-56)/(9+8)=-29/17

d.

8. We need to check only at x=0 for continuity as both the functions are continous in thier domain

6x-6 at x=0 and x^2+6x-6 at x=0 should be equal for it to be continous at x=0

6(0)-6=-6

0^2-6(0)-6=-6

Function is continous everywhere

b.

9. Average rate of change=[f(9)-f(1)]/[9-1]=(81+56-1-7)/8=129/8

e.

11.f(g(x))=1/sqrt(x+1)

f(g(3))=1/2

g(f(x))=sqrt((1/x)+1)

g(f(3))=sqrt(1/3+1)=2/sqrt(3)

b.

12 expression=[f(1+h)-f(1)]/h=[1/(h+2)-1/2]/h=(2-h-2)/h.2.(h+2)=-h/h.2.(h+2)=-1/(2h+4)

a

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