This table shows a linear relationship between the amount of water in a 30-gallon tank and time

Question

Time(minutes). Water(gallons)

0. 6.

5 12

10 18

Answer 1

Use any two points on the table and the slope formula to find the rate of change:

m = y₂ -y₁/x₂-x₁ = (18-12)/(10-5) = 6/5 gallons per minute_.

Therefore, the water is going into the tank at a rate of 6/5 gallons per minute or 1.2 gallons per minute.

Use the point-slope formula to write an equation for the line: y-y₁ = m(x-x₁)

You need to use the slope, and one point from the table.

m = 6/5 I am using the point (0,6) therefore y₁=6 and x₁=0

y-y₁ = m(x-x₁)

y-6 = 6/5(x-0)

y-6 = 6/5x

y= 6/5x + 6 This is the equation in slope-intercept form.

We see from the equation (and from the point (0,6)) that the y-intercept is 6. This means that the tank started with 6 gallons of water before being filled with additional water

Hope this helps.