1. what is the slope of the line in the graph show below? (image) a. -2 b. -1 c. 1 d. 2 2. find the slope of a line that passes through (-2,-3), and (1,1). 3. for the equation -4y = 8x, what is the constant of variation? 4. suppose y varies directly with x, and y = 24 when x = 8. what is the value of y when x = 10? 5. what is an equation for the line with slope 2/3 and y-intercept 9? 6. what is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)?

The line intercepts points (0,3) and (1,1).

We can find the slope using its formula

Therefore, the slope is -2. The right answer is A.

To find the slope, we apply the same formula as we did in the first question

Therefore, the slope is 4/3.

To find the constant of variation, we need to express the given linear equation in the form . That is, we need to isolate

Where and .

Therefore, the constant of variation is -2.

This problem is setting a proportionality, that is, the raltion between the first pair of coordinates is the same for the second pair.

So, if y = 24 when x = 8, that means y-values are triple than x-values, because 8x3 = 24.

Now, if x = 10, then y = 3x10 = 30.

Therefore, the missing value is y = 30.

To find the equation, we use the slope-intercept formula

Where is the slope and is the y-intercept.

In this case, we have and .

Replacing these values, we have

First, we need to find the slope

Then, we use the point-slope formula

Therefore, the slope-intercept form is

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