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Find the linear function with the following properties:

a) y = mx + b
b) y = ax² + bx + c
c) y = mx² + b
d) y = a/x + b

User Evadne Wu
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1 Answer

1 vote

Final answer:

The student's question is about identifying which of the provided equations represents a linear function. The correct equation that fits the linear form y = mx + b is Option a, as it matches the definition of a linear equation with a slope m and a y-intercept b.

Step-by-step explanation:

The student has asked to find the linear function that satisfies certain properties. A linear function is generally of the form y = mx + b, where m is the slope and b is the y-intercept. Let's analyze the given options:

  • Option a: y = mx + b - This is indeed the slope-intercept form of a linear equation, representing a straight line.
  • Option b: y = ax² + bx + c - This represents a quadratic equation, not a linear function.
  • Option c: y = mx² + b - This is also a quadratic equation because of the x² term.
  • Option d: y = a/x + b - This is an inverse variation, not a linear equation.

Practice Test 4 Solutions 12.1 states that linear equations are of the form y = b + mx, which is simply a reordering of y = mx + b (Option a). Hence, the correct option that describes a linear function is Option a. Based on the given reference material, answers in option D (A and B - A. y = -3x and B. y = 0.2 +0.74x) from Practice Test 4 are also linear equations, but these do not match the exact y = mx + b form initially described in the student's question.

User Greg Weber
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