Calculate the rate of change over the interval of -10 < x < -6 of the graph.

The rate of change over the interval of -10 < x < -6 of the graph is 2

Step-by-step explanation:

In the given figure:

The relation between x and y over the interval of -10 < x < -6, represented by a line, then the rate of change over this interval is the slope of the line

∵ The line passes through points (-10, -6) and (-6, 2)

∴ x1 = -10 and y1 = -6

∴ x2 = -6 and y = 2

→ Substitute them in the rule of the slope above

∴

∴ The slope of the line = 2

∵ The rate of change = the slope of the line

∴ The rate of change over the interval of -10 < x < -6 of the graph is 2

{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

47 - 90 = 43

43 - 180 = x

x = 137