Question

PLEASE PLEASE PLEASE HELP ME!

Answer 1

Answer: 50 Minutes = 309 gal

Step-by-step explanation: Every 10 minutes the amount of water goes up by 18, so after 50 minutes the water would be equivalent to 309 gallons.

Answer 2

Answer:

$y=1.8x+219$

309 gallons

Step-by-step explanation:

So to find the linear equation, we can use the data from the table.

First, use the data from the table to find the slope. Pick any two points. I'm going to use (10,237) and (20,255).

Let (10,237) be x₁ and y₁ and let (20,255) be x₂ and y₂.

The formula for slope is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\frac{255-237}{20-10}$

Simplify:

$m=18/10=1.8$

Thus, the slope is 1.8. This means that 1.8 gallons of water flow into the tank every minute.

Now, let's find the slope-intercept. To do this, we can use the point-slope form. The point-slope form is:

$y-y_1=m(x-x_1)$

Let's use (10,237) for consistency. Plug in 237 for y₁  and 10 for x₁. Also use 1.8 for m. Thus:

$y-237=1.8(x-10)$

Distribute:

$y-237=1.8x-18$

Add 237 to both sides:

$y=1.8x+219$

What this means is that there is initially 219 gallons of water in the tank already. Every minute, 1.8 gallons is added further.

And that's our linear equation :)

So, to find the amount of gallons after 50 minutes, plug in 50 for x and solve:

$y=1.8(50)+219\\y=90+219=309$

After 50 minutes, there will be 309 gallons of water.