In Exercises 77-78, give the slope and y-intercept of each line whose equation is given. Assumethat B ≠ 0. Ax = By - C

Verified step by step guidance

1. Rewrite the given equation in the standard form of a line, which is \( Ax + By = C \).
2. Rearrange the equation to solve for \( y \) in terms of \( x \). This involves isolating \( y \) on one side of the equation.
3. Divide every term by \( B \) to express \( y \) in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
4. Identify the slope \( m \) from the equation \( y = mx + b \). It will be the coefficient of \( x \).
5. Identify the y-intercept \( b \) from the equation \( y = mx + b \). It will be the constant term.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly identifying the slope and y-intercept of a line, allowing for easy graphing and analysis of linear relationships.

Rearranging Linear Equations

To find the slope and y-intercept from the given equation Ax = By - C, it is often necessary to rearrange the equation into slope-intercept form. This involves isolating y on one side of the equation, which may require adding or subtracting terms and dividing by coefficients to express y in terms of x.

Understanding Slope and Y-Intercept

The slope of a line indicates its steepness and direction, calculated as the change in y over the change in x (rise/run). The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. Both concepts are fundamental in analyzing linear equations and their graphical representations.