Question

Write the inequality for the graph

Answer 1

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: $m=\frac{y_2-y_1}{x_2-x_1}$   where you substitute/plug in two points on the line

or using this  $m=\frac{rise}{run}$

"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