Problem 64 Explain how to graph an equation... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 64

Explain how to graph an equation in the rectangular coordinate system.

Short Answer

Expert verified

Graphing an equation in the rectangular coordinate system involves understanding the coordinate system, identifying the equation to be plotted, finding the slope and y-intercept from the equation, and drawing a straight line through the points determined by the slope and y-intercept. For our given example, the line graph of the equation $y = 3x - 2$ intercepts the y-axis at -2 and rises 3 units for each unit moved to the right.

Step by step solution

Understand the rectangular coordinate system

Before starting to graph anything, we first need to understand the rectangular coordinate system. It is composed of two perpendicular number lines: the horizontal line called $x$-axis and the vertical line called $y$-axis. The intersection of the two axes is the point called the origin, where both $x$ and $y$ coordinates equal to 0. The location of every point in this system can be described by an ordered pair of numbers, $(x, y)$, where the first number represents the $x$-coordinate (horizontal position relative to the origin) and the second number represents the $y$-coordinate (vertical position relative to the origin).

Identify the equation

Identify the equation you are tasked with graphing. For our example, let's use a linear equation in its slope-intercept form $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept. The slope tells how steep the line is, and the y-intercept tells where the line crosses the y-axis.

Determine the slope and y-intercept

From the chosen equation, determine the values of the slope and the y-intercept. The slope is the number in front of the $x$ and the y-intercept is the number added or subtracted from $mx$. For example, in $y = 3x - 2$, the slope is 3, and the y-intercept is -2.

Plot the y-intercept

On the graph, find the value of the y-intercept on the y-axis and put a dot. In our example, put a dot on -2 on the y-axis.

Use the slope to find the next point

Starting from the y-intercept, use the slope to find the next point. In our example, the slope is 3, which means for every 1 unit increase in $x$, $y$ increases by 3 units. So, from the y-intercept (-2), go right 1 unit (increase in $x$) and up 3 units (increase in $y$) and mark another dot.

Draw the line

Once you have two or more points, you can draw a straight line through them. This line represents the graph of the equation.

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91影视

Explain how to graph an equation in the rectangular coordinate system.

Short Answer

Step by step solution

Understand the rectangular coordinate system

Identify the equation

Determine the slope and y-intercept

Plot the y-intercept

Use the slope to find the next point

Draw the line

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