Question

in a linear equation of the form $y = mx + b$, $m$ represents the select choice and $b$ represents the select choice.

Explanation:

Step1: Recall linear equation form

In the slope - intercept form of a linear equation \(y = mx + b\), by definition, \(m\) is the slope (or the rate of change) of the line. This is because the slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}\) for two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line, and in the equation \(y=mx + b\), the coefficient of \(x\) is this slope.

Step2: Recall the meaning of \(b\)

The value \(b\) in the equation \(y=mx + b\) is the \(y\) - intercept. The \(y\) - intercept is the point where the line crosses the \(y\) - axis. Mathematically, when \(x = 0\), \(y=b\), so the point \((0,b)\) is on the line, which is the \(y\) - intercept.

Answer:

For the first "Select Choice" (corresponding to \(m\)): slope (or rate of change)
For the second "Select Choice" (corresponding to \(b\)): \(y\) - intercept