Question

What is the x-intercept of the trend line, y = -0.13x + 11.2? Is that possible in a real-world situation? Explain.

A) The x-intercept is 85.4, and it's possible in a real-world situation.
B) The x-intercept is 11.2, and it's possible in a real-world situation.
C) The x-intercept is 0.13, and it's possible in a real-world situation.
D) The x-intercept is 0, and it's not possible in a real-world situation.

Answer 1

The x-intercept of the trend line y = -0.13x + 11.2 is found by setting y to zero and solving for x, which results in an x-intercept of approximately 85.4; this is possible in a real-world situation depending on the context.

Step-by-step explanation:

The x-intercept of a line is the point at which the line crosses the x-axis, which is when the value of y is zero. For the equation y = -0.13x + 11.2, to find the x-intercept, you would set y to zero and solve for x:

0 = -0.13x + 11.2

-11.2 = -0.13x

x = 86.154 (approximately 85.4 when rounded to one decimal place)

Therefore, the correct answer is A) The x-intercept is 85.4, and it is possible in a real-world situation depending on the context of the data represented by the equation.

For example, in a business context, if x represents time in months and y represents profit in thousands of dollars, a negative x-intercept would not be meaningful since you can't have negative time.

However, if x represents a quantity that can be negative, like temperature changes, then an x-intercept at 85.4 could be possible.

Answer 2

The correct x-intercept of the trend line y = -0.13x + 11.2 is 86.15, which is not listed among the provided options. Real-world applicability of an x-intercept depends on the context, which is not given in the question.

Step-by-step explanation:

Finding the x-intercept of a Linear Equation

The x-intercept of a linear equation is the value of x at which the line crosses the x-axis, meaning the y value is 0. In the equation y = -0.13x + 11.2, to find the x-intercept, we set y to 0 and solve for x:

0 = -0.13x + 11.2

0.13x = 11.2

x = 11.2 / 0.13

x = 86.15

Real-world Application: Whether an x-intercept is possible in a real-world scenario depends on the context of the data represented by the equation. In some cases, such as time-based scenarios, having a year 0 may not make sense, since there's no such 'starting' year. Nevertheless, the concept of an x-intercept still holds mathematically even if the corresponding scenario doesn't allow for a year 0.

Answering the student's multiple-choice question, none of the provided options are correct. The actual x-intercept calculated is 86.15, which was not one of the options given. So while the math to find the x-intercept is straightforward, the provided answer choices do not match the correct calculation. As for the real-world applicability, the x-intercept concept can be real, but it depends on the context of the data, which is not provided in this question.