What side do you shade in an inequality?

Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line. For a vertical line, larger solutions are to the right and smaller solutions are to the left.

What happens when a line passes through the origin?

If the line cuts directly through the origin, this means that at one point, one of these coordinates is equal to zero. In the figure above, notice how the coordinates of the third line will not be equal to zero.

What does it mean when a point passes through the origin?

A circle passing through the origin means that the origin, i.e., the point (0,0), lies on the circle. In other words, (0,0) satisfies the equation of the circle.

What does the shaded part of a graph mean?

This is a graph of a linear inequality: The inequality y ≤ x + 2. You can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2.

What is the equation of the line that passes through the origin?

y = mx
In general, therefore, the equation y = mx represents a straight line passing through the origin with gradient m. The equation of a straight line with gradient m passing through the origin is given by y = mx .

How do you find the inequality of a shaded region?

Since the shaded area is below the x-axis, the first inequality is y≤0, since we wish to include the boundary of the shaded area. Since the shaded area is to the right of the y-axis, the second inequality is x≥0. The shaded region is above the line y=−1, so the third equation is y≥−1.

What does the line under the inequality mean?

The “Greater than or equal to” symbol is used in linear inequalities when we don’t know whether the value of a variable is greater than or equal to a particular value. It is expressed by the symbol ” ≥ “. The sleeping line below the greater sign means “equal to”.