Which of the following is an equation of the line through (11, –3) and (7, 9)?

y = -3x + 30.

Step-by-step explanation:

The slope of line = (9- (-3)) / (7 - 11)

= 12/-4

= -3.

We use the point-slope form of a straight line:

y - y1 = m(x - x1)        where m = slope = -3 and (x1, y1) = (7, 9)

y - 9 = -3(x - 7)

y - 9 = -3x + 21

y = -3x + 21 + 9

y = -3x + 30.

You haven't supplied a list of possible answers so the correct answer might not  be in the above form but will be equivalent to it.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places