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You water the plants in your classroom at a constant rate. After 5 seconds, your watering can contains 58 ounces of water. Fifteen seconds later, the can contains 28 ounces of water.

AWrite an equation in slope-intercept form that represents the amount yy (in ounces) of water in the can after xx seconds.

Verified Answer :

Answer:

y = -3x + 142

Step-by-step explanation:

We can write the information given to us as ordered pairs, where x represents the number of seconds and y represents the amount of water in the can:

(5, 58) and (15, 28)

To write an equation in slope-intercept form, first we find the slope.  The formula for slope is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Using our points, we have

\(m=\frac{28-58}{15-5}=\frac{-30}{10}=-3\)

We use point-slope form to write the initial equation:

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

Using our first point as (x₁, y₁), we have:

y-58 = -3(x-28)

Using the distributive property, we have

y-58 = -3(x)- -3(28)

y-58 = -3x+84

Adding 58 to each side, we have

y-58 + 58 = -3x+84+58

y = -3x + 142

Answer:

The equation of the line is y=-3x+72 . Below is the detailed explanation about the steps.

Step-by-step explanation:

Given:

    After 5 seconds, your watering can contains 58 ounces of water.

    After 15 seconds, it contains 28 ounces.

To find:

    The equation of line in slope-intercept y=mx+b form.

Let's get the two points from given information which are (5, 58) and (15,28)

Use slope formula to find slope of the line.

        Slope m =\(\frac{y2-y1}{x2-x1}\)

Using the points,

          m=\(\frac{28-58}{15-5}\)

           m=\(\frac{-30}{10}\)

           m=-3

Slope of the line is -3. Plugin this value into equation y=mx+b for 'm'

y=-3x+b

Use one of the point to find 'b'. Let's use (5,58)

Plug in this point into the y=-3x+b

   58= -3(5) +b

   58=-15+b

Add both sides 15.

   72=b

So, equation of the line in slope intercept form is y= -3x+72.

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