At 6: 00 a. m., there were 800,000 gallons of water remaining in a reservoir. after 8 hours of irrigation, there were 100,000 gallons of water remaining. write a linear equation that describes the number of gallons of water remaining as a function of the time the field had been irrigated.

WR(t) = 800000 - 87500t

Explanation:

t is the time in hours.

WR(t) is the Water Remaining as a function of the time, in gallons.

WR(t) = 800000 - 87500t

Explanation:

t is the time in hours.

WR(t) is the Water Remaining as a function of the time, in gallons.

WR(t) = 800000 - 87500t

Explanation:

t is the time in hours.

WR(t) is the Water Remaining as a function of the time, in gallons.

The problem states the initial amount of water in the reservoir is 800000 gallons.

Then we need to find the amount of water spent each hour. For this we know that after 8 hours, 100000 gallons remain.

In other words:

800000 - 100000 = 700000 gallons have been spent in 8 hours.

Which gives a ratio of 700000 / 8 = 87500 gallons per hour.

Writing all together, the linear equation is built by taking the initial amount of water and subtracting the ratio of water spent, multiplied for the time variable:

WR(t) = 800000 - 87500t

question says to graph a triangle (xyz) and reflect it over the line y=x to create triangle x'y'z'.

we know that line y=x has both coordinates equal like (1,1), (5,5) etc so we can easily graph that reflecting line.

description of transformation:

we can see that x and y coordinate gets switched after transformation like (2,8) changed to (8,2)

what do you notice about the two line segments you drew:

we see that line segments xp and x'p are of same length and perpendicular to the reflecting line y=x.

do you think you would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line? :

yes, i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line.

how do you know? :

by measuring the length of yk and y'k.