Math Problem Statement

What is the value of the function at x=−2?

Responses

y=−2 y equals negative 2

y = 0 y = 0

y = 2

y = 2

y = 3 y = 3 A coordinate grid with x and y axis ranging from negative five to five. The line passes the points begin ordered pair negative 2 comma 2 end ordered pair and begin ordered pair 2 comma negative 3 end ordered pair.

Solution

To determine the value of the function at x=−2x = -2, we can use the given information about the line passing through the points (−2,2)(-2, 2) and (2,−3)(2, -3).

Since the point (−2,2)(-2, 2) is provided, and this point lies on the line, the value of the function when x=−2x = -2 is simply the y-coordinate of that point.

Thus, the value of the function at x=−2x = -2 is y=2y = 2.

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Here are 5 related questions:

  1. How do you find the equation of a line passing through two points?
  2. What is the slope of the line passing through (−2,2)(-2, 2) and (2,−3)(2, -3)?
  3. How would you calculate the y-intercept of the line based on these points?
  4. What is the value of the function at x=2x = 2?
  5. How can you graph a linear function given two points?

Tip: To calculate the slope of a line between two points, use the formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)

Theorems

Line Equation Theorem

Suitable Grade Level

Grades 6-8

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