Question

Solutions in the coordinate plane.

6x+2y>−2

a. Identify the slope.
b. Identify if the line is dashed or solid.
c. Identify if you shade above or below the line.

Answer 1

The slope is negative, the line is solid, and we shade below the line.

Step-by-step explanation:

a. The slope of the line can be found by rearranging the equation into the slope-intercept form y = mx + b, where m is the slope. In this case, rearranging 6x + 2y > -2a to y > -3x - a gives us a slope of -3. Therefore, the slope is negative.

b. The line is solid, not dashed. This is because the inequality symbol in the equation is >, which represents a strict inequality, meaning the line should be solid to indicate that the points on the line are included in the solution.

c. To determine whether to shade above or below the line, we can choose a test point. Let's choose the origin (0,0). Substitute its coordinates into the inequality. 6(0) + 2(0) > -2a simplifies to 0 > -2a.

Since 0 is not greater than a negative number, we shade below the line.