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what is the slope of the line –6y + 2x = 18 in simplest form?

-6y + 2x = 18

Subtract 2x to both sides:

-6y = -2x + 18

Divide -6 to both sides:

y = -2/-6x - 3

Simplify:

y = 1/3x - 3

Now it's in the form of y = mx + b, where 'm' is the slope.

So the slope here is 1/3.

First of all, I would like to thank Cosmos for deleting my incorrect answer. (applause)

Now, we will proceed to our main program.

Manipulate -6y + 2x = 18 into the y = mx + b form.

Subtract 2x from both sides
-6y = -2x + 18

Divide both sides by -6


Simplify


The slope will be the coefficient of x.

7a)

-The rate of growth is the slope,  which is 1/2 a foot a year

-We can set up the equation in y=mx+b form, where y is the total height and x is the number of years. m is the rate of growth and b is the height of the plant at 0 years (aka the y-int) which is 4 ft. Substitute in the values into the equation to get y=0.5x+4

7b)

-The rate of speed is the slope, which is 175/4 or 43.75 miles per hour.

-Use the same y=mx+b formula for the equation, where y is the total distance and x is the number of hours. m is the rate of speed, but it will be negative because the slope of the line is negative. The rate of speed is 43.75 miles per hour but the slope will be -43.75. b is the distance from home at 0 hours (the y-int), which is 175 miles.

The equation will be y= -43.75x+175

8a)

-The rate of speed from 0 to 3 hours (the slope) is 50 mph.

8b)

-The rate of speed from 3 to 4 hours was 0 mph because there is no slope and no distance was traveled.

8c)

-The rate of speed from 4 to 9 hours was 60 mph.

8d)

-The average overall rate of speed (total distance divided by total time) is 450 miles divided by 9 hours, which is 50 mph.