- #1
mathdad
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The slope of y = x is 1.
Why is this the case?
Why is this the case?
MarkFL said:Suppose we pick two distinct points on the line:
\(\displaystyle P_1(a,a)\) and \(\displaystyle P_2(a+h,a+h)\) where $0\ne h$
Then:
\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{a+h-a}{a+h-a}=\frac{h}{h}=1\)
MarkFL said:Suppose we pick two distinct points on the line:
\(\displaystyle P_1(a,a)\) and \(\displaystyle P_2(a+h,a+h)\) where $0\ne h$
Then:
\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{a+h-a}{a+h-a}=\frac{h}{h}=1\)
RTCNTC said:I am having trouble reading your replies. Your Latex "hides" behind your words in bold letters.
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The words "and" and "where" are blocking the two points you talk about in your reply. Can you fix this problem? Talk to the owner of the site.
I like Serena said:I have the same problem on my Samsung Android phone in both Chrome and the native browser.
MathJax re-renders 3 or 4 times in different fonts and spacings and ends up in a smaller font for which insufficient space is reserved.
When I tilt my screen to landscape it's still wrong, but when I refresh it, it ends up almost okay.
I've made a screenshot but the dialog to upload it doesn't work on Android. Anyway, it looks exactly as RTCNTC described.
If I switch to the mobile style it renders correctly with the proper font size. The mobile style is just not feasible though. It is too limited in its features.
MarkFL said:You can deactivate the Fast Preview via the MathJax menu. Right-click any equation and go to Math Settings -> Math Renderer -> Fast Preview and turn that off. Please let me know if tis resolves the issue on your mobile device. :D
I like Serena said:Unfortunately there's no right-click on Android, and the closest thing to it (long press) pops up a different menu.
Now that I know about it, I've disabled Fast Preview on my regular computer - faster loading times and less jumping (I think), yay!
Is there any other way to switch it off?
A quick google doesn't help, other than explaining it can apparently be configured on the server-side.
MarkFL said:No right-click? Wow...I knew those pocket gadgets were relatively limited, but didn't know they are that bad. (Bug)
MarkFL said:It can be disabled sitewide, but I don't know if this is something the majority wants. (Bandit)
MarkFL said:I might be able to handle this myself without bothering Jameson, as I also know a thing or two about vBulletin and implementing $\LaTeX$ by MathJax on web pages.. :D
First, what OS/browser are you using, because no one else has reported any issues with my posts.
MarkFL said:Okay, I have disabled the fast preview globally, since mobile devices don't allow disabling it locally. Let me know if this resolves the issue. :D
MarkFL said:Suppose we pick two distinct points on the line:
\(\displaystyle P_1(a,a)\) and \(\displaystyle P_2(a+h,a+h)\) where $0\ne h$
Then:
\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{a+h-a}{a+h-a}=\frac{h}{h}=1\)
MarkFL said:Okay, I have disabled the fast preview globally, since mobile devices don't allow disabling it locally. Let me know if this resolves the issue. :D
MarkFL said:Okay, I have disabled the fast preview globally, since mobile devices don't allow disabling it locally. Let me know if this resolves the issue. :D
I like Serena said:...Unfortunately it doesn't solve the issue. The spacing is still wrong. (Worried)
MarkFL said:That is unfortunate, but is an issue that needs to be addressed either by MathJax, or better, by the manufacturers of the mobile browsers. I like to use the metaphor of riding a tricycle on the interstate highway for mobile devices accessing the internet. Rather than redesign the highway, I would say the tricycles need to be improved instead. :D
MarkFL said:That is unfortunate, but is an issue that needs to be addressed either by MathJax, or better, by the manufacturers of the mobile browsers. I like to use the metaphor of riding a tricycle on the interstate highway for mobile devices accessing the internet. Rather than redesign the highway, I would say the tricycles need to be improved instead. :D
I like Serena said:I can see that the problem is known, for instance here:
MathJax and Android's Chrome bug - Mathematics Meta Stack Exchange
Unfortunately it doesn't offer a solution.
The slope of the line y = x is 1. This is because the equation is in the form y = mx + b, where m is the slope and b is the y-intercept. Since there is no number in front of the x, the slope is assumed to be 1.
To find the slope of the line y = x, you can use the slope formula: (y2 - y1) / (x2 - x1). Since the equation y = x has the same value for y and x, any two points on the line will have the same coordinates. This means that (x1, y1) and (x2, y2) can be any two points on the line, and the slope will always be 1.
A slope of 1 means that for every 1 unit increase in the x-coordinate, there is also a 1 unit increase in the y-coordinate. This forms a 45-degree angle with the x-axis, and the line goes up 1 unit for every 1 unit it goes to the right. It also means that the line has a constant rate of change of 1.
Yes, the line y = x is a straight line. This is because it has a constant slope of 1 and does not have any breaks or changes in direction. It is a perfect diagonal line that extends infinitely in both directions.
The slope of the line y = x is significant because it represents the rate of change of the line. In real-life applications, this can represent things like speed, growth, or change in a physical quantity. It also helps determine the direction of the line and how steep or gradual it is.