This week in Precalc 11, I learned about linear inequalities with the formula y=mx+b
We know that “m” represents the slope of the line and that “b” represents the y-intercept.
So for the symbols of equalities we need to know that (>) is the symbol for greather than, (<) is the symbol for less than, (≥) is the symbol for greater or equal to, (≤) is the symbol for less than or equal to. Let’s take a look at some equations using the formula y=mx+b while using the symbols.
We’re going to use the same base equation so that we can analyze the differences easily
Let’s start with our base line which is y=2x+3
Slope of 2 and y-intercept of 3
As we can see the shaded area is our solutions for our y-intercept.The solutions(shaded area) is under the line because the solutions are less than the line (2x+3). We can see that the line is dotted since the solutions of y do not include the points on the line.
But when we change the symbol to less than or equal to, the line becomes solid because y can equal the coordinates of the line.
The same concept applies to the opposite symbols. We can see that for y is bigger, the area that is shaded is above the line. And again, the line is dotted as y cannot equal the coordinates of the line.
The same thing applies for this as well. The line becomes solid as the solutions can equal the coordinates of the line.
