after 2 hours, there are 1,400 ml of fluids remaining in a patients iv. the fluids drip at a rate of 300 ml…

after 2 hours, there are 1,400 ml of fluids remaining in a patients iv. the fluids drip at a rate of 300 ml per hour. let x be the time passed, in hours, and y be the amount of fluid left in the iv, in ml. write a linear function that models this scenario.\nthe slope of the line is \nthe y - intercept of the line is \nthe linear function is

after 2 hours, there are 1,400 ml of fluids remaining in a patients iv. the fluids drip at a rate of 300 ml per hour. let x be the time passed, in hours, and y be the amount of fluid left in the iv, in ml. write a linear function that models this scenario.\nthe slope of the line is \nthe y - intercept of the line is \nthe linear function is

Answer

Explanation:

Step1: Determine the slope

The fluid is dripping at a rate of 300 mL per hour, so the amount of fluid is decreasing. The slope $m$ of the linear - function representing the amount of fluid left over time is - 300 (negative because the amount of fluid is decreasing). $m=-300$

Step2: Find the y - intercept

We know that after $x = 2$ hours, $y=1400$ mL. Using the point - slope form $y - y_1=m(x - x_1)$ and the point $(x_1,y_1)=(2,1400)$ and $m=-300$. First, we can also use the slope - intercept form $y=mx + b$. Substitute $x = 2$, $y = 1400$ and $m=-300$ into $y=mx + b$: $1400=-300\times2 + b$ $1400=-600 + b$ $b=1400 + 600=2000$

Step3: Write the linear function

The slope - intercept form of a linear function is $y=mx + b$. Substituting $m=-300$ and $b = 2000$ into the equation, we get $y=-300x + 2000$.

Answer:

The slope of the line is - 300. The y - intercept of the line is 2000. The linear function is $y=-300x + 2000$.