Question

A glass bottle filled with oil weighs 590590 grams. After Sophia uses 200200 milliliters of oil, the bottle of oil weighs 400400 grams. The weight MM of the bottle of oil, in grams, is a function of VV, the volume, in milliliters, of oil Sophia has used. Write the function's formula.

Answer 1

M = -0.95V+590... Make sure the V is capitalized. Khan will mark it wrong if it isn't.

Explanation:

m = 400-590/ 200-0

= -190/200

= -19/20

= -0.95

M = -.095+590

Answer 2

`M=-0.95V+590`

Explanation:

Let M be the weight of the bottle of oil in grams and V be the volume , in millimeters of oil Sophia has used.

As weight M of the bottle of the oil is a function of V, the volume , in ml of oil Sophia has used. This means weight of bottle depends on the volume of oil used.

We have been given that a glass bottle filled with oil weighs 590 grams. This means that initial weight of bottle or y-intercept is 590 and point (0,590) represents the initial amount.

We have been given that after Sophia uses 200 milliliters of oil, the bottle of oil weighs 400 grams. This means that when volume (V) of oil is 200 ml, the weight (M) of the bottle of oil 400 grams.

As weight of bottle is decreasing after using the oil, so our function will be a linear function.

Since we know that equation of a line in slope-intercept form is
`y=mx+b`, where m represents slope and b represents y-intercept or initial value.

Let us find the slope of line using points (0,590) and (200,400).

`\text{ Slope (m)}=(y_2-y_1)/(x_2-x_1)`

`\text{ Slope (m)}=(400-590)/(200-0)`

`\text{ Slope (m)}=(-190)/(200)`

`\text{ Slope (m)}=(-19)/(20)`

`\text{ Slope (m)}=-0.95`

Upon substituting our values in slope intercept form of equation we will get our function as:

`M=-0.95V+590`

Therefore, the function
`M=-0.95V+590` represents the weight (M) of the bottle of oil, in grams, as a function of the volume (V), in milliliters, of oil Sophia has used.