Problem 38 - Understanding Elementary Algebra with Geometry

Question

Sketch the graph of the given equation. Label the intercepts. $$y=-1$$

Step-by-Step Solution

Answer

Draw a horizontal line at y = -1 and label the point (0, -1) on the y-axis.

Step 1 - Determine the type of graph

The equation given is in the form of y equals a constant, which represents a horizontal line. In this case, the horizontal line is where y = -1.

Step 2 - Identify the y-intercept

To determine the y-intercept, observe where the line intersects the y-axis. Since the line is given by y = -1, it intersects the y-axis at -1.

Step 3 - Locate the y-intercept on the graph

On the graph, place a point on the y-axis at y = -1. This is the y-intercept.

Step 4 - Draw the horizontal line

From the y-intercept (0, -1), draw a straight horizontal line across the graph. This line will be parallel to the x-axis since it represents y = -1.

Step 5 - Label the intercept

Finally, label the intercept (0, -1) on the graph to indicate where the line crosses the y-axis.

Key Concepts

horizontal line

A horizontal line is a straight line that moves left to right and is parallel to the x-axis.
In the equation \(y = -1\), the value of \(y\) is the same no matter what the value of \(x\) is.
When you see an equation where \(y\) is equal to a constant, you know you are dealing with a horizontal line.
This is because y does not change; it remains fixed at the constant value.

y-intercept

The y-intercept is where the graph of a line crosses the y-axis.
For the equation \(y = -1\), the y-intercept is at the point (0, -1).
To find the y-intercept, you can set \(x\) to 0 and solve for \(y\).
In this equation, \(y\) is already given as -1, so the intercept is straightforward.
On the graph, mark a point where \(y = -1\) and \(x = 0\).

graph sketching

Graph sketching involves drawing the graph of an equation based on its form.
For the equation \(y = -1\), you start by noting it's a horizontal line.
Locate the y-intercept at (0, -1) and make a point there.
Then, draw a line straight across from left to right at \(y = -1\)
This will form a horizontal line that does not slope up or down.

equation of a line

An equation of a line shows a relationship between the \(x\) and \(y\) coordinates on a graph.
For horizontal lines like \(y = -1\), the equation is simple.
The \(y\)-value remains constant and there is no \(x\) term affecting it.
This makes it easy to graph because you don't need to calculate slopes or other points.
Simply draw a horizontal line where \(y\) is equal to the given constant.