Question

select the correct equations. identify all of the linear functions. -x³ = 3y + 10; 2x + 5y = 13; 3(2x⁴ + y) = 14; y = 13 - 2x²; 2 = y + x⁶; y = x + 7

Explanation:

Step1: Recall linear function form

A linear function has the form \(y = mx + b\) (or \(Ax + By = C\) for linear equations), where the highest power of variables is 1.

Step2: Analyze each equation

• \(-x^3 = 3y + 10\): Has \(x^3\) (degree 3) → Not linear.
• \(2x + 5y = 13\): Can be rewritten as \(y = -\frac{2}{5}x + \frac{13}{5}\) (degree 1) → Linear.
• \(3(2x^4 + y) = 14\): Has \(x^4\) (degree 4) → Not linear.
• \(y = 13 - 2x^2\): Has \(x^2\) (degree 2) → Not linear.
• \(2 = y + x^6\): Has \(x^6\) (degree 6) → Not linear.
• \(y = x + 7\): Is \(y = 1x + 7\) (degree 1) → Linear.

Answer:

The linear functions (equations) are \(2x + 5y = 13\) and \(y = x + 7\) (and also the initially selected \(y = x + 7\) and the correct \(2x + 5y = 13\) from the analysis). So the correct ones to select are the boxes with \(2x + 5y = 13\) and \(y = x + 7\).