When the inequality sign is < / > (less than/greater than), the line is a dotted line.
When the inequality sign is ≤ / ≥ (less than or equal to/greater than or equal to), the line is a solid line.
If "y > " (y is greater than...), the shaded area is above the line.
If "y < " (y is less than...), the shaded area is below the line.
The equation of an inequality is similar to the slope-intercept form.
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
The slope(m) can be found by either:
Slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where you substitute/plug in two points on the line
or using this [tex]m=\frac{rise}{run}[/tex]
"rise" is the number of units you go up(+) or down(-) from each point
"run" is the number of units you go to the right from each point.
When you look at the graph, from each distinguished point you go down 1 unit, and to the right 1 unit. So the slope is -1.
When x = 0, y equals 1, so the y-intercept is 1.
You know:
m = -1
b = 1
The sign is ≤ / ≥ because it's a solid line
"y < " because the shaded area is below the line
y ≤ -x + 1
