Question

question 1-5
the us department of agriculture monitors the amount of high fructose corn syrup americans consume in a year. the relationship can be represented by the equation ( y = -1.4x + 64 ) where ( x ) is the number of years, and ( y ) is the number of pounds the average american consumes each year.
complete the statement about the linear relationship.
the y-intercept means that (square) the amount of high fructose corn syrup consumed by the average american is (square).

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) occurs when \(x = 0\). In the context of this problem, \(x\) represents the number of years, and \(y\) represents the pounds of high fructose corn syrup consumed.

Step2: Substitute \(x = 0\) into the equation

Given the equation \(y=-1.4x + 64\), when \(x = 0\) (which means 0 years after the start of the monitoring or at the initial time of monitoring), we substitute \(x = 0\) into the equation: \(y=-1.4(0)+64\).
Simplifying the right - hand side, we get \(y = 64\). So when \(x = 0\) (the number of years is 0, or at the start), the amount of high fructose corn syrup consumed is 64 pounds.

Answer:

The y - intercept means that when the number of years \(x = 0\) (at the start of monitoring), the amount of high fructose corn syrup consumed by the average American is 64 pounds.
So the first blank should be filled with "when the number of years is 0 (at the start)" and the second blank should be filled with "64 pounds".