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Describe how the graphs of y=x and y=x-15 are related

Isn't it obvious, don't ya think Isn't it obvious, don't ya think answered

The slopes of both lines are the same: 1.

So, I think they are parallel.

Graph both to double-check.

oobleck oobleck answered

y=x-15 is the line y=x, shifted down 15 units

Step-by-Step Bot Step-by-Step Bot answered

The graphs of y=x and y=x-15 are related in the sense that they both represent linear functions with a slope of 1. The graph of y=x is a straight line passing through the origin (0,0) and has a slope of 1.

When the constant term in the equation is subtracted by 15 in y=x-15, the graph is shifted downwards by 15 units compared to y=x. This means that for every x-coordinate, the y-coordinate of the graph is decreased by 15 units.

In other words, the graph of y=x-15 is simply the graph of y=x shifted 15 units downwards.

Explain Bot Explain Bot answered

To understand how the graphs of y=x and y=x-15 are related, let's start by talking about the equation for each graph.

The graph of y=x represents a straight line with a slope of 1 and a y-intercept of 0. This means that for every unit increase in x, the value of y also increases by 1. The line passes through the origin (0,0) and extends infinitely in both the positive x and y directions.

Now, let's look at the equation for y=x-15. This equation represents another straight line, but with a slope of 1 and a y-intercept of -15. In this case, for every unit increase in x, the value of y increases by 1, but it starts 15 units below the x-axis, effectively shifting the whole line downward.

So, the graphs of y=x and y=x-15 are related in two ways:

1. Parallel: Both lines have the same slope of 1. This means that their steepness is the same. They will never intersect or cross each other.

2. Vertical Shift: The graph of y=x-15 is obtained by taking the graph of y=x and shifting it downward by 15 units. This shift aligns the y-intercept at -15 instead of 0.

So, in summary, the graphs of y=x and y=x-15 are parallel lines with the same slope, but the latter graph is shifted downward by 15 units compared to the former graph.