Question

Please Someone smart help me with this!!

Answer 1

See below

Explanation:

The linear function is to be expressed in slope-intercept form:

y = mx + c

where:

m = slope

=
`(y_(2) -y_(1))/(x_(2) -x_(1))`

Select a pair of x and y coordinates of two points along this graph

e.g (0,1) and (5,0):

m =
`((0 - 1)Percent InDecimal)/((5 - 0) hour)`

=
`(-1)/(5)`

∴ slope =
`-(1)/(5)` =
`-0.2(PercentInDecimal)/(hour)`

which means 0.2 × 100%= 20%

∴The slope indicates that the power decreases by 20% per hour

c = y-intercept:

It is the y-value AT which the graph cuts or meets the y-axis. Its corresponding x-coordinate is 0. The y-intercept can be either read directly from the graph or calculated mathematically

∴y-intercept = 1

In this scenario, the y-intercept indicates the initial value or the value present in the beginning.
which means 1.0 × 100% = 100%
∴The y-intercept indicates that the battery is at 100% when you turn on the laptop.

∴Linear function relating y to x:

Substituting the values of m and c into the above stated equation:

`y = -(1)/(5)x + 1`

The x-intercept is the x-value at which the graph crosses or intersects the x-axis. It’s corresponding y-coordinate is zero.

x-intercept = 5

In this scenario, the x-intercept indicates the point at which the final value is reached or achieved.

∴ The x-intercept indicates that the battery lasts 5 hours.

The battery power is at 75% =
`(75)/(100)` = 0.75 (expressed in decimal form. This means y = 0.75, which is to be substituted into the above derived linear function to solve for the corresponding value of x:

`0.75 = -(1)/(5)(x) + 1`

Rearrange the equation to isolate x and make it the subject of the equation:

`(1)/(5)x = 1 - 0.75`

`(1)/(5)x = 0.25`

Cross-multiplication is applied:

`(1)(x) = (5)(0.25)`

x = 1.25 hours

∴The battery power is at 75% after 1.25 hours