Question

were you paying attention? i sure hope so! a.) ( m = \frac{y_2 - y_1}{x_2 - x_1} ) b.) ( y - y_1 = m(x - x_1) ) c.) ( ax + by = c ) d.) ( y = mx + b )

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), which matches option a.

Step2: Analyze other options

• Option b: \( y - y_1 = m(x - x_1) \) is the point - slope form, not the slope formula.
• Option c: \( ax+by = c \) is the standard form of a linear equation, not for slope calculation.
• Option d: \( y=mx + b \) is the slope - intercept form, not the slope formula.

Answer:

a. \( m=\frac{y_2 - y_1}{x_2 - x_1} \)