Question

module
select the correct button in the table to show whether each equation is linear or nonlinear.
y=7(4^x)
27x - 13y = 42
4y + 2x = 3
9.25x² + 2.75y² = 35
y=7x + 10
linear nonlinear linear nonlinear linear nonlinear

Explanation:

Step1: Recall linear equation form

A linear equation in two variables is of the form \(Ax + By = C\) (standard) or \(y = mx + b\) (slope - intercept), where \(A\), \(B\), \(C\), \(m\), \(b\) are constants and the exponents of \(x\) and \(y\) are 1. For a single - variable or exponential/quadratic etc., it's non - linear.

Step2: Analyze \(y = 7(4^{x})\)

The equation \(y = 7(4^{x})\) has a variable \(x\) in the exponent. Since the exponent of \(x\) is not 1, it is a non - linear equation. So we connect it to the "Nonlinear" button.

Step3: Analyze \(27x-13y = 42\)

The equation \(27x - 13y=42\) is in the standard form of a linear equation \(Ax+By = C\) (where \(A = 27\), \(B=- 13\), \(C = 42\)) with the exponents of \(x\) and \(y\) equal to 1. So it is a linear equation. We connect it to the "Linear" button.

Step4: Analyze \(4y + 2x=3\)

The equation \(4y + 2x = 3\) can be rewritten in the form \(Ax+By = C\) (\(A = 2\), \(B = 4\), \(C = 3\)) with the exponents of \(x\) and \(y\) equal to 1. So it is a linear equation. We connect it to the "Linear" button.

Step5: Analyze \(9.25x^{2}+2.75y^{2}=35\)

The equation \(9.25x^{2}+2.75y^{2}=35\) has \(x\) and \(y\) with exponents equal to 2. Since the exponents are not 1, it is a non - linear equation. We connect it to the "Nonlinear" button.

Step6: Analyze \(y = 7x+10\)

The equation \(y = 7x + 10\) is in the slope - intercept form of a linear equation \(y=mx + b\) (where \(m = 7\), \(b = 10\)) with the exponent of \(x\) equal to 1. So it is a linear equation. We connect it to the "Linear" button.

Answer:

• \(y = 7(4^{x})\) connects to Nonlinear.
• \(27x-13y = 42\) connects to Linear.
• \(4y + 2x=3\) connects to Linear.
• \(9.25x^{2}+2.75y^{2}=35\) connects to Nonlinear.
• \(y = 7x + 10\) connects to Linear.