Question

Determine whether each equation represents a linear or non-linear function. Select linear or non-linear for each question.

a) y = 3x + 7
b) y = x^2 - 5x + 9
c) y =√x + 2
d) y = 2^x

Answer 1

Equation a) y = 3x + 7 is linear while b) y = x^2 - 5x + 9, c) y =√x + 2, and d) y = 2^x are all non-linear equations.

Step-by-step explanation:

To determine whether each equation represents a linear or non-linear function, we need to analyze the form of each equation:

• a) y = 3x + 7: This equation is linear because it's in the form of y = mx + b, where 'm' is the slope, and 'b' is the y-intercept.
• b) y = x^2 - 5x + 9: This equation is non-linear because it includes a term with x raised to the power of 2, making it a quadratic equation.
• c) y =√x + 2: This equation is non-linear since it involves the square root of x, which does not produce a straight line graph.
• d) y = 2^x: This equation is non-linear because it describes an exponential function, where the variable x is the exponent, leading to a curve that is not a straight line.

So, for each equation:

1. y = 3x + 7 is a linear equation.
2. y = x^2 - 5x + 9 is a non-linear equation.
3. y =√x + 2 is a non-linear equation.
4. y = 2^x is a non-linear equation.