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).
$3 y+5=0$

Key Concepts

Slope-Intercept Form

A fundamental way to express the equation of a line is the slope-intercept form, written as y = mx + b. In this form, m represents the slope (or steepness) of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis. This form makes it straightforward to identify the line's key characteristics and to graph it.

Slope

The slope of a line is a measure that indicates how steep the line is. By definition, it is the ratio of the change in the y-coordinate to the change in the x-coordinate between two distinct points on the line. When a line has a constant y-value, such as in a horizontal line, the slope is zero, indicating that there is no vertical change as the horizontal coordinate changes.

Y-Intercept

The y-intercept of a line is the point where the line crosses the y-axis, meaning it is the value of y when x is equal to zero. This value gives an initial condition for the line and is particularly useful when graphing the equation since it provides a starting point from which the slope can be applied to locate additional points on the line.

Graphing Linear Equations

Graphing linear equations involves plotting the y-intercept on the coordinate plane and then using the slope to determine another point on the line. Once two points are plotted, a straight line can be drawn through them. Graphing provides a visual representation of the line and is useful for verifying algebraic results. Additionally, graphing utilities facilitate this process by allowing one to input an equation and visually confirm its slope and y-intercept.

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