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,
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.
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