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In the context of graphing linear equations, the x-intercept is the point where the line crosses the x-axis.
By definition, this happens when the value of y is zero.
Mathematically, if you have an equation of the form \(y = mx + b\), you set y to 0 and solve for x.
To make it clearer, let’s explore step 4 in our example equation: y - 5 = 0.
Since the equation simplifies to y = 5, it's clear that y is always 5, regardless of x.
This means that the line never crosses the x-axis, therefore, there is no x-intercept for the equation y = 5.
This concept is crucial as it helps us understand not only how and where lines intersect axes, but also ensures we correctly interpret the specific scenarios where no x-intercept exists.

The y-intercept is the point where the line crosses the y-axis.
This occurs when x = 0.
In other words, it's the value of y when x is zero.
Using our example equation y - 5 = 0, we can determine this by substituting x with 0.
In our case, the equation simplifies to y = 5.
This lets us know that the y-intercept is at the point (0, 5).
To articulate, regardless of the x value, y remains constant at 5.
Thus, when graphing this line, we can plot a point at (0, 5) and draw the line horizontally through this point.
Understanding y-intercepts gives students fundamental insight into how a graph is positioned relative to the y-axis.

A horizontal line in graphing is a straight line that has the same y-value for every point along it.
In other words, it doesn't matter what x is, y remains constant.
In our example, the horizontal line is represented by the equation y = 5.
This indicates that for any value of x, y will always be 5.
To graph this, you simply draw a straight line across the graph at y = 5.
It’s important to remember that horizontal lines have a slope of 0 since they don’t rise or fall as they move horizontally.
This concept helps cement the idea that not all linear equations change values constantly – some maintain a single value despite variations in x.