Problem 56 Graph each linear equation. $$... [FREE SOLUTION]

Chapter 3: Problem 56

Graph each linear equation. $$ x-4=0 $$

Short Answer

Expert verified

A vertical line passing through x = 4.

Step by step solution

Rewrite the Equation

Rewrite the given linear equation in a more standard form. The equation is given as $ x - 4 = 0 $, which simplifies to $ x = 4 $.

Identify Key Characteristics

Identify that the equation $ x = 4 $ is a vertical line. Vertical lines have undefined slopes and run parallel to the y-axis.

Plot the Line on the Graph

On a coordinate plane, draw a vertical line that passes through $ x = 4 $. This means every point on this line will have the x-coordinate of 4, such as $(4, 0)$, $(4, 1)$, $(4, -1)$, etc.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

vertical line

A vertical line on a coordinate plane is a line that goes straight up and down. Unlike other lines, it does not tilt or curve. It means that no matter how high or low you go on the line, the x-coordinate remains the same. For example, in the equation $ x = 4 $, every point on this line will have 4 as the x-coordinate, like $ (4, 0)$, $ (4, 2) $, or $ (4, -5) $.
Vertical lines are always parallel to the y-axis.
To remember: any equation in the form $ x = a $ represents a vertical line passing through the point $ (a, 0) $.

undefined slope

The slope of a line measures how steep the line is. But for vertical lines, the concept of slope doesn't work the same way. Since a vertical line goes straight up and down, there is no 'run' to calculate the slope.
Remember, slope is defined as 'rise over run' - the change in y divided by the change in x. For a vertical line, the change in x is 0 which gives us a division by zero scenario, hence the slope is said to be undefined.
Always note that vertical lines have an undefined slope because the line does not have a horizontal direction.

coordinate plane

The coordinate plane is a two-dimensional surface where we can graph points, lines, and curves. It consists of two axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
Each point on the plane has a pair of coordinates $ (x, y) $, which tells you where the point is located in relation to the axes.
To plot a line like $ x = 4 $ on the coordinate plane, you look for the line passing through all points where the x-coordinate is 4. This line will be parallel to the y-axis.
Therefore, understanding the coordinate plane is essential for accurately graphing equations and interpreting their graphs.

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91影视

Graph each linear equation. $$ x-4=0 $$

Short Answer

Step by step solution

Rewrite the Equation

Identify Key Characteristics

Plot the Line on the Graph

Key Concepts

vertical line

undefined slope

coordinate plane

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