Math Problem Statement

The linear function f(x) generates the ordered pairs shown in the table.

Drag and drop the numbers below into the boxes to complete the sentence. 1 2 3 4 5

The function that models the data in the table is f(x) = x +

Solution

To determine the function f(x)=mx+bf(x) = mx + b that models the data in the table, we would need to analyze the relationship between the values of xx and f(x)f(x) (or yy) given in the ordered pairs.

However, since you haven't provided the specific table, I can explain how to generally find the values for mm (the slope) and bb (the y-intercept):

  1. Find the slope (m): The slope is the change in f(x)f(x) divided by the change in xx, which can be calculated using the formula: m=f(x2)f(x1)x2x1m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
  2. Find the y-intercept (b): Once the slope is known, you can substitute one of the ordered pairs into the equation f(x)=mx+bf(x) = mx + b and solve for bb.

To help you complete the sentence "The function that models the data in the table is f(x)=_x+_f(x) = \_x + \_," I would need the values in the table or ordered pairs.

Could you share the ordered pairs or more details from the table?


Here are 5 questions based on this concept:

  1. How do you calculate the slope of a linear function from two points?
  2. What does the slope represent in the context of a linear function?
  3. How can you determine the y-intercept from a given table of values?
  4. Why is it important to find both the slope and the intercept when modeling data?
  5. How do changes in slope affect the graph of a linear function?

Tip: The slope tells you how steep the line is, while the y-intercept tells you where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

f(x) = mx + b
m = (f(x2) - f(x1)) / (x2 - x1)

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8