Xpress Taxi Service charges $1.50 per minute traveled minus $0.25 per minute spent in stopped traffic. You only have $10 in your wallet, so that is the maximum amount you can spend on your ride. In which quadrant(s) would the graph represented by this situation fall?
Let's graph the following inequalities.
First, change the inequality into slope-intercept form. Remember, that if you have to divide or multiply by a negative number, you must flip the inequality sign.
Now, we need to determine the shading. You can use one of two methods to do this. The first way is to use the graphs and forms from above. The equation, in slope-intercept form, matches up with the purple dashed line and shading. Therefore, we should shade above the dashed blue line.
This inequality is already in slope-intercept form. So, graph the line, which will be solid, and then determine the shading. Looking at the example graphs above, this inequality should look like the red inequality, so shade below the line.
Let's determine the linear inequality that is graphed below.
Earlier, you were asked to find which quadrant(s) into which the graph represented by the situation would fall.
To solve this taxi cab problem, we must first set up an inequality to represent the situation.
You can't travel a negative number of miles or sit in traffic for a negative number of minutes. Therefore both x and y must have zero or positive values. When both x and y are positive, the graph occurs in the first quadrant only. Graph the function to check this answer.
First, change the inequality into slope-intercept form.
Now, we need to determine the type of line and shading. Because the sign is “<,” the line will be dashed and we will shade below.
What is the equation of the linear inequality?
Graph the following inequalities.
y>x−5 3x−2y≥4 y<−3x+8 x+4y≤16 y<−2 y<−12x−3 x≥6 8x+4y≥−20 −4x+y≤7 5x−3y≥−24 y>5x y≤0
Determine the equation of each linear inequality below.
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 2.11.