Exercise 14 Page 119

&Verbal Score &&Math Score &x ≤ 1200 && y≤ 1200 To graph these inequalities, we will first determine the boundary lines. They can be determined by replacing the inequality symbol with the equals sign. ccc & &Inequality &Boundary Line &Verbal Score: &x ≤ 1200 &x = 1200 &Math Score: &y ≤ 1200 &y = 1200 The boundary line of the verbal score will be a vertical line where all the points on it have the x-value of 1200. The other line will be a horizontal line where all the points on it have the y-value of 1200. Since the verbal and math scores cannot be negative, the lines will be bound by the axes.

The inequality x≤ 1200 says that the x-coordinates of the points are less than or equal to 1200. Therefore, we will shade the region to the left of the line x=1200. It is the same for y≤1200. The region below the line will be shaded.

Next, we will graph x+y≥ 1700 by finding its boundary line. &Inequality &&Boundary Line &x+y ≥ 1700 &&x+y = 1700 Now we will rewrite the equation in slope-intercept form. Thus, we can immediately identify its slope and y-intercept to make the sketch bit easier. &Boundary Line &&Slope-Intercept Form &x+y = 1700 &&y=-1x+1700 We will plot the y-intercept and find a second point using the slope to draw a line.

Next, we will connect the points with line segment. The line will be solid because the inequality is non-strict.

In the final step, we will test an arbitrary point to decide which region we should shade. We will test the point (0,0) to make the math bit easier.

The point did not satisfy the inequality, so we will shade the region that does notcontain the point.

The overlapping area will be our solution.