Question

Help Please! (Answer Will Receive Metal)

Find The Rate & Explain How You Found The Rate Of Change For The Following.

(Will Upload Picture)

Answer 1

Alright...so we have

x = 2 and y = 10

when x goes up 2.....y goes up 10......because next we have

x = 4 and y = 20

What would happen if we only went up by 1 though? well...since we know this is a linear system...we know if we only go up halfway in the 'x'...we will only go up halfway in the 'y'

so if we start at x = 2 and y = 10

and we go up 1 instead of 2...

x = 3....now y will = 15

So it looks like every time x goes up 1....y goes up 5 ...so our rate of change....is 5

Answer 2

^ that was for the first one you uploaded lol

Answer 3

The second one..we have an equation...and want to see what the slope is...well we want this in slope intercept form for that

\[\large 5x + 3y = -2\]

subtract 5x from both sides of the equation

\[\large 3y = -5x - 2\]

and divide everything by 3

\[\large y = -\frac{5}{3}x - \frac{2}{3}\]

the coefficient of the 'x' is our slope....the rate of change...so that one is -5/3

Answer 4

Now the third one...we have 2 points we can see....

at x = 3....y = 25

and

at x = 6 ...y = 50

so when x goes up 3....y goes up 25

Well we can use the slope formula to solve for that

\[\large \frac{y_2 - y_1}{x_2 - x_1}\]

plug in what we have

\[\large \frac{50 - 25}{6 - 3} = \frac{25}{3}\]

the rate of change for that...is 25/3

Answer 5

Jesh you're good! lol thank you so much! & yes it did help a lot!