Question

Graph the equation. $$ y=-\frac{1}{2} x-3 $$

   Graph the equation.
$$
y=-\frac{1}{2} x-3
$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 4, Problem 32

Instant Answer

Solved by Expert Amy Jiang

09/04/2020

Step 1

The equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. Here, m = -1/2 and b = -3. Show more…

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Graph the equation. $$ y=-\frac{1}{2} x-3 $$

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Key Concepts

Linear Equation

A linear equation represents a straight line when graphed on the coordinate plane and is typically in the form y = mx + b. This equation form shows the relationship between two variables where each increment in x results in a constant change in y.

Slope

The slope of a line is a measure of its steepness and direction. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A negative slope indicates that the line declines as x increases.

Y-intercept

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. It provides a starting point for graphing the line and is a key component of the slope-intercept form of a linear equation.

Slope-Intercept Form

This form of a linear equation, written as y = mx + b, directly reveals the slope (m) and y-intercept (b) of the line. It is widely used because it simplifies the process of graphing and understanding the behavior of the line on a coordinate plane.

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