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The graph shows the total mass as a function of the number of grapefruits. What is the slope of the best-fit line? What does this value mean? Predict the mass of 8 grapefruits.​

The Graph Shows The Total Mass As A Function Of The Number Of Grapefruits What Is The Slope Of The Bestfit Line What Does This Value Mean Predict The Mass Of 8 class=

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dsdrajlin

The slope of the best-fit line for the graph showing the total mass as a function of the number of grapefruits is 0.5 kg/grapefruit. The mass of 8 grapefruits is 4 kg.

We can represent the relationship between the number of grapefruits (x) and their total mass (y) using a linear equation.

[tex]y = mx + b[/tex]

where,

  • m: slope
  • b: y-intercept

Given 2 points, we can calculate the slope using the following expression.

[tex]m = \frac{\Delta y }{\Delta x}[/tex]

For instance, let's take points (1, 0.5) and (2, 1).

[tex]m = \frac{\Delta y }{\Delta x} = \frac{1-0.5}{2-1} = 0.5[/tex]

Now, let's use point (1, 0.5) in the linear equation to calculate the y-intercept.

[tex]y = mx + b\\\\0.5 = 0.5 \times 1 + b\\\\b = 0[/tex]

The resulting linear equation is:

[tex]y = 0.5x[/tex]

When we have 8 grapefruits (x = 8), their mass is:

[tex]y = 0.5(8) = 4[/tex]

The slope of the best-fit line for the graph showing the total mass as a function of the number of grapefruits is 0.5 kg/grapefruit. The mass of 8 grapefruits is 4 kg.

Learn more: https://brainly.com/question/2263981

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