+4 1. Find a linear inequality with the following solution set. Each grid line represents one unit.
[asy]
size(200);
fill((-5,-4)--(4,5)--(-5,5)--cycle,yellow);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i if(abs(i) >0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i if(abs(i) >0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
draw((-5,-4)--(4,5),dashed+red,Arrows(size=axisarrowsize));
rr_cartesian_axes(-5,5,-5,5);
for( int i = -4; i <= 4; ++i) {
draw((i,-5)--(i,5));
draw((-5,i)--(5,i));
}
[/asy]
2. Find a linear equality with the following solution set. Each grid line represents one unit.
[asy]
size(200);
fill((-0.5,-5)--(5,-5)--(5,5)--(4.5,5)--cycle,yellow);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i if(abs(i) >0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i if(abs(i) >0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
draw((-0.5,-5)--(4.5,5),red,Arrows(size=axisarrowsize));
rr_cartesian_axes(-5,5,-5,5);
for( int i = -4; i <= 4; ++i) {
draw((i,-5)--(i,5));
draw((-5,i)--(5,i));
}
[/asy]
