The table shows the percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer. A. Write and graph a linear function that relates y to x

B. Interpret the slope , the x-intercept , and the y intercept

C. After how many hours is the battery power at 75%?

Step-by-step explanation:

Let the equation of the function is,

y = mx + b

Here, m = slope of the function

b = y-intercept

y-intercept of function is the y-value of a point where x = 0.

From the table given,

y-intercept 'b' = 1

Slope of the line passing through two points and is given by,

Slope =

Slope of the line passing through (2, 6) and (4, 2) will be,

Slope =

          =

Equation of the line will be,

y = -2x + 1

B). Slope of the line = -2

x-intercept of the line (at y = 0),

y = -2x + 1

0 = -2x + 1

x =

y-intercept of the line = 1

y-intercept indicates that the power of the battery was 100% when we turn on the laptop.

C). Equation of the line is,

y = -2x + 1

Here, y = power remaining

x = Hours

For y = 75% ≈ 0.75

0.75 = -2x + 1

0.75 - 1 = -2x

-0.25 = -2x

x = 0.125

Therefore, after 0.125 hours battery power will be 75%.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: