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Chapter 1: Problem 11

Given the equation \(y=4 x-3\), answer the following questions. a. If \(x\) increases by 1 unit, what is the corresponding change in \(y\) ? b. If \(x\) decreases by 2 units, what is the corresponding change in \(y\) ?

Short Answer

Expert verified
a. \(4\) b. \(-8\)

Step by step solution

01

Analyze the linear equation

The given equation is a linear equation in the form \(y = mx + c\), where m is the slope and c is the y-intercept. In this case, the slope, m, is 4, and the y-intercept, c, is -3.
02

Find the change in y when x increases by 1 unit

Since slope m represents the rate of change of y with respect to x, we can find the change in y when x increases by 1 unit by multiplying the slope by the change in x. In this case, the change in x is 1, so the change in y is: \(\Delta y = m \times \Delta x = 4 \times 1 = 4\). The corresponding change in y when x increases by 1 unit is 4.
03

Find the change in y when x decreases by 2 units

Similarly, we can find the change in y when x decreases by 2 units. In this case, the change in x is -2, so the change in y is: \(\Delta y = m \times \Delta x = 4 \times (-2) = -8\). The corresponding change in y when x decreases by 2 units is -8. So the answers to the given questions are: a. The corresponding change in y when x increases by 1 unit is 4. b. The corresponding change in y when x decreases by 2 units is -8.

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