Please guide me to draw this : graph of $x \geq 5$ and $y \geq 5$

Question

how can I draw the graph for this

the graph of $x \geq 5$ and $y \geq5$ is?

please guide me to draw it

thanks in advance

Answer 1

the region in the upper right hand corner of the cartesian plane with a corner at $(5, 5)$ and bounded by the vertical line $x = 5$ and by the horizontal line $y = 5.$

edit: here is some explanation of how we arrive at this picture. to make it easier, we will start with the number line. once you have picked the origin, th unit, and increasing direction, we can plot the region $x \ge 5$ as the half line starting at the point and running to the right without an end. this is usually denoted by $[5, \infty).$ likewise, you can represent the region $1 \le x \le 2$ as the line segment between the points $1$ and $2$ is denoted by $[1,2].$ when you move on to the plane where we have two number line orthogonal to each other, $x$-line and the $y$-line. to plot the region containing all points $(x, y)$ so that $x \ge 5$ and $y \ge 5$ the points on the $x$-lines now become lines parallel to the $y$-line and same for the point on the $y$-lines. the common region where these lines meet is the picture you want.

i hope this helps.

Answer 2

Instead of beginning with the inequalities $y\geq 5$ and $x\geq 5$, begin instead by drawing the equations $y=5$ and $x=5$.

The line $y=5$ is the line where everywhere on it you have a $y$ value of $5$ and $x$ can by anything, i.e. it is a horizontal line. Similarly, the line $x=5$ is vertical.

To graph these as inequalities instead, take note of which side the inequality is facing. If you are ever confused, then test a point. Good points will all lie on the same side of the line (or more complicated curve in general). 6 is bigger than 5, so you want to include all points above the line $y=5$ to graph $y\geq 5$. Similarly for $x\geq 5$. In the image below, the inequality in $y$ is pictured with red with a lightly shaded region, and $x$ in blue.

To complete the picture, note that we are curious where $y\geq 5$ and $x\geq 5$, so it is where it is shaded by both inequalities simultaneously, pictured below in purple. Keeping in mind that the graph extends infinitely in each direction, the shaded purple part is the set of all points $(x,y)\in\mathbb{R}^2$ such that $x\geq 5$ and $y\geq 5$.

Once you become more comfortable with equations and such, you might opt to skip one or more of the steps to arrive at the answer more quickly, such as opting not to lightly shade each region and only shade the good region, or even skipping the step to draw the basic lines in the first place.

The only final thing I will mention is the difference in graphing this where you use $\geq$ signs and the case where they are replaced by $>$ signs instead, it is common practice to use dashed lines to denote the fact that the points along the line are not included in the region.