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Chapter 3: Problem 52

Graph each linear equation. $$ y=3 $$

Short Answer

Expert verified
The graph of \( y = 3 \) is a horizontal line passing through \( y = 3 \).

Step by step solution

01

Identify the equation type

The given equation is a horizontal line equation: \( y = 3 \). This means that for all values of \( x \), the \( y \) value remains constant at 3.
02

Plot points on the graph

Since \( y = 3 \) is a horizontal line, select any values for \( x \). The \( y \) coordinate will always be 3. For example, plot the points (0, 3), (2, 3), and (-2, 3).
03

Draw the line

Once the points are plotted, draw a straight horizontal line through them. This line represents the equation \( y = 3 \).

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Key Concepts

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

horizontal line
A horizontal line in geometry means the line runs parallel to the x-axis. For any horizontal line, the y-coordinate remains constant, while the x-coordinate can be any value. This is seen in the equation of the form y = c, where c is a constant. Unlike other lines where both x and y vary, a horizontal line's y-value does not change no matter how far you move left or right. Understanding this concept makes it easier to draw and interpret these lines on the graph.
plotting points
Plotting points is an essential skill in graphing equations. Points are plotted as ordered pairs (x, y). For our equation y = 3, start by choosing any x-values. For example, select x = 0, 2, and -2. Then pair these x-values with the y-value of 3, forming the points (0, 3), (2, 3), and (-2, 3). Plot these pairs on the graph by locating their position using the grid lines. This visual representation helps to bring the equation to life, showing exact locations the equation covers.
linear equation
Linear equations can be represented in various forms, but a common format is y = mx + b. For a horizontal line, however, the linear equation simplifies to y = c, where the slope m is 0. This suggests no change in y as x changes. Splitting linear equations into types helps in better understanding and graphing. The primary focus is to notice whether they describe horizontal (constant y) or vertical (constant x) lines, or lines that slope up or down. Knowing this, one can correctly plot and interpret any linear equation.

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Most popular questions from this chapter

Graph each linear equation. $$ y=-\frac{2}{3} x-2 $$

\(5 x-3 y=-2\) \(3 x-5 y=-8\)

Write an equation of the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form. (8,5) and (9,6)

Write an equation of the line satisfying the given conditions. Give the final answer in slope-intercept form. (Hint: Recall the relationships among slopes of parallel and perpendicular lines.) Passes through (2,3) parallel to \(4 x-y=-2\)

Find the \(x\) - and \(y\) -intercepts for the graph of each equation. $$ y=\frac{1}{3} x-2 $$
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