The base of the triangle lies on a horizontal line. Therefore, the equation of this boundary line is y= k, where k is the y-coordinate of its points. Since the line passes through the points (- 2, - 3) and (6, - 3), its equation is y= - 3. Moreover, the shaded region is above the line and the line is solid. This means the inequality sign is ≥.
y≥ -3
Inequality (II)
Let's treat one of the sides of the triangle as a line, paying close attention to the slope.
To travel from (2,5) to (6,- 3) on this boundary line we move 4 units in the positive horizontal direction and 8 units in the negative vertical direction. Since we know the run is 4 and the rise is - 8, we can find the slope.
Now that we know the slope of the line is - 2, we can partially write its equation in slope-intercept form.
y= - 2x+b
To find the y-intercept b we will use the fact that the line passes through (2,5). Let's substitute 2 and 5 for x and y, respectively, into the partial equation above and solve for b.
Now that we know that b= 9, we can write the equation of the boundary line.
y=- 2x+ 9
To determine the inequality sign we will use a point that belongs to the shaded area.
When substituted into the inequality, the point (3,- 2) must produce a true statement. Note that since the line is solid the inequality will not be strict.
