Give the slope and y-intercept of each line whose equation is given. Assume that B ≠ 0. Ax = By - C

Verified step by step guidance

1. Start with the given equation: \(Ax = By - C\).
2. Rearrange the equation to solve for \(y\) in terms of \(x\). Add \(C\) to both sides and then divide both sides by \(B\): \(By = Ax + C \implies y = \frac{A}{B}x + \frac{C}{B}\).
3. Identify the slope \(m\) from the equation in slope-intercept form \(y = mx + b\). Here, the slope is \(m = \frac{A}{B}\).
4. Identify the y-intercept \(b\) from the equation. The y-intercept is the constant term \(b = \frac{C}{B}\).
5. Summarize: The slope of the line is \(\frac{A}{B}\) and the y-intercept is \(\frac{C}{B}\).

Key Concepts

Slope-Intercept Form of a Line

The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. Converting a given equation into this form helps identify these values directly.

Rearranging Linear Equations

To find the slope and y-intercept from an equation like Ax = By - C, you must isolate y on one side. This involves algebraic manipulation such as adding, subtracting, and dividing terms to rewrite the equation in slope-intercept form.

Slope and Y-Intercept Definitions

The slope measures the steepness of a line, calculated as the ratio of vertical change to horizontal change. The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.