# Does Slope Matter? Comparing the Graphs of y=1/x and y=5/x+6

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The graphs of y=1/x and y=5/x+6 are quite different. The first graph is a straight line, while the second has an upward slope. How do these two graphs compare? Let’s start by looking at how each one changes as x gets larger or smaller (by looking at their slopes). If you look closely, you’ll see that the graph of y=1/x will always be steeper than the graph of y=5/x+6. This means that if we take any point on either curve and move it vertically up or down from its original position on the x-axis, then this new position will correspond to a higher value for 1/(x) than 5/(x+y).

The line y=x is the easiest example of a straight-line graph. The slope of this graph at any x value will always be positive, and its steepest point (the highest change in height between values on one side to those on the other), occurs right when x = 0. This means that if we take any point on this curve and move it vertically up or down from its original position on the x-axis, then this new position will correspond to an increase in absolute value for some number starting with x to t+s where s ≥0 . If you look closely, you’ll see that while our first equation’s slope stays constant as x increases, the second one changes more dramatically. In this graph of y = x, for example, the slope changes from sloping upwards to level with a value of 0 at x=0 and then becomes much more steep as you move further right.

### Which one is better?

-The second equation has higher slopes than first equation in areas where it curves up sharply enough to cross over the horizontal axis. It also crosses over zero on its way down which means that there’s no limit to how high or low our function can climb if we start out near a point that intersects this line twice (or more).

-This lack of limits makes it so all points along the curve will have positive values regardless of how far away they are from either endpoints. This contrasts with our previous straight line which always has a slope of zero, meaning that any point along the line will have a y value with an absolute value less than or equal to 0.

-If we are using this equation in conjunction with other equations on our graph, it may be beneficial for us to choose one with the highest slopes possible so that if there is ever an area where our function goes from being negative to positive (or vice versa) then all points nearby would also change accordingly and we wouldn’t need as many lines intersecting each other. Conversely, if you’re trying to create smooth curves instead of sharp angles then choosing equations closer to x=0 might work best since they’ll never cross over – but these won’t give you as much control over how quickly the graph moves up or down.

-Ultimately, how you choose your equation for graphing is going to depend on what kind of trend line you’re trying to create and one can’t always be better than another – it really comes down to preference. That said, there are some trends that can be easily detected by looking at the equation. If you’re trying to show how y increases as x is increasing then a line of y=mx+b might work best for you since this will have the highest slopes possible so that if there is ever an area where our function goes from being negative to positive (or vice versa) then all points nearby would also change accordingly and we wouldn’t need as many lines intersecting each other.

-Conversely, if you’re trying to create smooth curves instead of sharp angles then choosing equations closer to x=0 might work best since they’ll never cross over – but these won’t give you as much control over how quickly the graph moves up or down.

-It’s also worth noting that choosing the higher slope will make it more difficult to graph from left to right, while a low slope can be drawn in “turtle steps” without too much difficulty.

-For example: y=x^y might give you an equation with very high slopes and this would let you have greater control over how your function moves up or down but if we were graphing between negative infinity on the x axis all the way past positive infinity then instead of drawing one line from -infinity to +infinity we’d need many lines intersecting each other which is not as easy for a human brain like ours to try and plot out.