7.) Construct a function with a rate of change of and an initial value of -3. (put your equation in slope-intercept form y = mx +b)

The function would be y = (1/3)x - 3

Step-by-step explanation:

The slope-intercept form is written in the form of y = mx + b where we leave "y" and "x" alone and plug in values for "m" and "b".

"m" is the rate of change while "b" is the initial value.  

In this case, the rate of change given is 1/3. Therefore, m = 1/3.

The initial value given is -3. Therefore, b = -3

To figure out the function, all we have to do is plug in the values that we found for both m and b into the slope-intercept form:

y = mx + b

y = (1/3)x + (-3)

When we simplify this equation, we get:

y = (1/3)x - 3

a is the correct

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1