WolframAlpha: How to plot a family of curves?

[epenguin]

just something I need quickly to illustrate a homework help, don't want to spend much time on.

What is the code in WolframAlpha just to plot an ornery family of curves?

Searched WA and find all sorts of fancy things, not this ornery one.

Should. be something like e,g.
For n= 1 to 20 c= n*0.05 plot f(x,y,c)

 

[mfb]

If you are fine with making the list yourself just type it in like that: plot c*x for c=0,0.1,0.2,0.3.

 

[epenguin]

Thank you. That will be much better than nothing. There must surely be a simple way to complete that listing automatically specifying just first value, interval, number of curves, last value.

Meantime I did find a quite convenient free app that doesn't even need to be downloaded, with specifically a curve family amongst its explicit options, and that has the advantage of having several colours https://www.mathe-fa.de/en#result - which was useful for the illustration I wanted Failure of uniqueness for this first-order differential equation. But routinely for looking into things it would be good to know how to do it on WolframAlpha..

 

[Bill Simpson]

Try this with WolframAlpha

plot Table[n*x^2+x-3,{n,1,8,1.5}] x= -3 to 5

 

[epenguin]

Thank you. That enabled me to plot a denser family of curves than I could before which is what I need to do, just for the purposes of making a didactic point.
It will take me a long time to master this program.
I need to modify your program to make all the curves black. This appears to involve "Plotstyle → Black" but wherever I put this it was not understood by the program. Also I want to be able to make the curves are thick as well as black. And I could do without the numerical table as I don't seem to be able to upload the resultIng picture without it, so the picture is tiny.
I would be grateful for your further help.