Linear inequalities are similar to the slope-intercept form, which is:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)
The difference is that the sign is not an equal sign, so instead of =, you use < , > , ≤ , ≥.
When the sign is ≤ or ≥ ("less/greater than or equal to") the line is a solid line.
When the sign is < or >, the line is a dotted line.
When y is > (greater than), the shaded area is above the line.
When y is < (less than), the shaded area is below the line.
BLUE LINE:
Since the line is a solid line, and the shaded area is above the line, the sign is ≥.
y ≥ mx + b
When x = 0, y is 2, so the y-intercept is 2.
y ≥ mx + 2
To find the slope, you can use the slope formula and find and plug in two points. Or you can use this:
[tex]slope=\frac{rise}{run}[/tex]
Rise is the number of units you go up(+) or down(-)
Run is the number of units you go to the right
If you look at the blue line, from each point, you go up 1 unit, and to the right 2 units. So the slope is [tex]\frac{1}{2}[/tex]
[tex]y\geq \frac{1}{2}x+2[/tex]
GREEN LINE:
The line is a solid line, and the shaded area is below the line, so the sign is ≤.
y ≤ mx + b
When x = 0, y is -1, so the y-intercept is -1
y ≤ mx - 1
If you look at the green line, from each point, you go up 1 unit, and to the right 3 units. So the slope is [tex]\frac{1}{3}[/tex].
[tex]y \leq\frac{1}{3} x-1[/tex]
