Spray a Line!!!

What: Sprinkle points along a 2D line and play Why: The equations and inequlities dealing with lines suddenly make better sense Time To Complete: 6 hours

pts2 is your friend the Line! In 2D, any equation of the form ax+by + c = 0 </Span> has solutions namely the x and y coordinates that satisfy the identity, namely lhs = rhs, line up along a fixed line specified by the three constants a, b and c. </Span>

//do not use the reserved word line, alter e.g. linear;

linear = 3*x+2*y-3;

//points residing on one side of the line;
pts1 = instance [linear < 0 and -5<x<5 and -5<y<5 , 50];

//points residing on the line;
pts2 = instance [linear == 0 and -5<x<5 and -5<y<5 , 50];

//points residing on the other side of the line;
pts3 = instance [linear > 0 and -5<x<5 and -5<y<5 , 50];

//make a list of colors to color the points in each region;
color[{red, black,green}];

//show all points;
pointplot pts1 also pts2 also pts3;

save as trash;

Output

Run the Free Form code again and you should each time get a different distbution of the scattered points.

Output