In Exercises 43-48, (a) find the slope and y-intercept (if...

In Exercises 43-48, (a) find the slope and $y$-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$-11-8 y=0$

Key Concepts

Graphing Linear Equations

Graphing linear equations involves plotting the y-intercept and using the slope to determine additional points on the line. This process provides a visual representation of the equation and aids in understanding its geometric properties.

Graphing Utility

A graphing utility, such as a graphing calculator or software, is used to verify the algebraic work by providing a plotted graph. This tool helps ensure the accuracy of the slope and y-intercept obtained through algebraic manipulation.

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying equations to convert them into a familiar form. For linear equations, rewriting in slope-intercept form makes it easier to identify the slope and y-intercept, which are essential for further analysis and graphing.

Slope-Intercept Form

The slope-intercept form is a way of writing a linear equation as y = mx + b, where m represents the slope and b is the y-intercept. This form is useful for quickly identifying these key properties of the line.

Slope

The slope of a line indicates its steepness and the direction it tilts. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line, and it helps determine how the line increases or decreases.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis. It serves as a starting point for graphing the line, and its value is directly visible in the slope-intercept form of a linear equation.

Please give Ace some feedback