Sunday, July 19, 2020

Linear Inequalities in Two Variables - Practice Problems and Answers (#3)

Problems: 

 Graph 4x + 9y ≤ 72 
Graph y < -3x + 21

 Answers:
Answer for 4x + 9y less than or equal to 72: Consider 4x + 9y = 72. x-intercept: Put y = 0 into 4x + 9y = 72. Get 4x = 72 i.e. x = 18 and so (18, 0) is a on the line. y-intercept: Put x = 0 into 4x + 9y = 72 to get 9y = 72 i.e. y = 8. So, (0, 8) is on the line. Check points: Try (0, 10): Since 4(0) + 9(10) = 90 is not less than or equal to 72, then don't shade above the line. Try (0,0). Since 4(0) + 9(0) = 0 is less than or equal to 72, shade where (0, 0) is at which is below the line 4x + 9y = 72. Now, we will draw the graph. Draw the Cartesian coordinate system and the line 4x + 9y = 72 which goes through the points (0, 8) and (18, 0). Make sure the line is solid. Shade below the line. Now, we will give the answer for the graph of y < -3x + 21. Consider y = -3x + 21. The x-intercept is (7, 0) and the y-intercept is (0, 21). Plot the line on the graph and make sure it is dashed due to the "<" sign since it does not have equality. Check points: Try (0,0). So, 0 < -3(0) + 21 = 21 is true and so we will shade where (0, 0) is at which is to the left of the line y = -3x + 21. Try (10, 0). So, 0 < -3(10) + 21 = -30 + 21 = -9 is false and we won't shade here.



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