Isn't it obvious, don't ya think
answered
So, I think they are parallel.
Graph both to double-check.
oobleck
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Step-by-Step Bot
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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
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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.
