TExES Mathematics 4-8 (115) Practice Test

To derive the slope-intercept form of a line's equation, you need to utilize the formula \(y = mx + b\), where \(m\) represents the slope of the line and \(b\) signifies the y-intercept.

In this case, you are given a slope of 3 and a y-intercept of -1. Substituting these values into the formula, you replace \(m\) with 3 and \(b\) with -1. This results in the equation:

\[y = 3x - 1\]

This formulation confirms that for every increase of 1 unit in \(x\), \(y\) increases by 3 units, hence capturing the slope accurately. Additionally, it indicates that the line crosses the y-axis at -1, aligning with the given y-intercept.

These specific values distinctly lead to the final equation, ensuring that the slope and y-intercept match the conditions of the problem accurately.