After filling the ketchup dispenser at the snack bar where she works, Kelley measures the level of ketchup during the day at different hourly intervals. Complete parts a to c. a. Assuming the ketchup is used at a constant rate, write a linear equation that can be used to determine the level of ketchup in the dispenser after x hours. Let y represent the level of ketchup in inches. nothing

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MrRoyal MrRoyal · Answer 1 · 2021-10-27T12:02:03+02:00

Linear functions are used to represent equations of straight lines

The linear equation is: [tex]\mathbf{y= - \frac{5}{8}x + 15}[/tex]

From the question (see attachment), we have:

[tex]\mathbf{(x_1,y_1) = (5,11\frac 78)}[/tex]

[tex]\mathbf{(x_2,y_2) = (8,10)}[/tex]

Calculate the slope (m) using:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{10 - 11\frac{7}{8}}{8-5}}[/tex]

[tex]\mathbf{m = \frac{- 1\frac{7}{8}}{3}}[/tex]

Express as improper fraction

[tex]\mathbf{m =- \frac{15/8}{3}}[/tex]

[tex]\mathbf{m =- \frac{5}{8}}[/tex]

The equation is then calculated as:

[tex]\mathbf{y= m(x -x_1)+ y_1}[/tex]

So, we have:

[tex]\mathbf{y= - \frac{5}{8}(x - 8) + 10}[/tex]

[tex]\mathbf{y= - \frac{5}{8}x + 5 + 10}[/tex]

[tex]\mathbf{y= - \frac{5}{8}x + 15}[/tex]

Hence, the linear equation is: [tex]\mathbf{y= - \frac{5}{8}x + 15}[/tex]

Read more about linear equations at:

https://brainly.com/question/11897796