At the beginning of spring, Anand planted a small sunflower in his backyard. The sunflower's height in inches, h, after w weeks, is given by the equation h=3.75 w+18. What could the number 3.75 represent in the equation? The rate of change in the sunflower's height. The sunflower's final height The sunflower's height after one week. The sunflower's height when it was planted.

Question

At the beginning of spring, Anand planted a small sunflower in his backyard. The sunflower's height in inches,  h, after  w weeks, is given by the equation  h=3.75 w+18. What could the number 3.75 represent in the equation? The rate of change in the sunflower's height. The sunflower's final height The sunflower's height after one week. The sunflower's height when it was planted.

Bytelearn · Accepted Answer

Analyze Equation: Analyze the given equation for the sunflower's height. The equation given is h = 3.75w + 18, where h is the height of the sunflower in inches and w is the number of weeks since Anand planted it.Identify Components: Identify the components of the equation. The equation is in the form of a linear equation y = mx + b, where m is the slope or rate of change, and b is the y-intercept. In this context, h corresponds to y (the dependent variable), 3.75 corresponds to m (the rate of change), w corresponds to x (the independent variable), and 18 corresponds to b (the initial value or y-intercept).Interpret Rate of Change: Interpret the meaning of the number 3.75 in the equation. Since 3.75 is multiplied by the number of weeks w, it represents the rate at which the sunflower's height increases each week. This is the amount the sunflower grows in height for each additional week.Determine Representations: Determine what 3.75 does not represent. 3.75 is not the final height of the sunflower, as the final height would depend on the number of weeks grown and would be represented by h when w is known. 3.75 is not the sunflower's height after one week, as that would be calculated by substituting w = 1 into the equation, which would give h = 3.75(1) + 18. 3.75 is not the sunflower's height when it was planted, as the height when it was planted is represented by the y-intercept, which is 18 in this equation.

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