A student draws the dashed line on a sheet of graph paper and shades the half-plane…
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Inequalities · Linear Inequalities
Problem
A student draws the dashed line 2x+y=4 on a sheet of graph paper and shades the half-plane that contains the point (3,0).
(i) Write the inequality that the student has represented.
(ii) Determine whether the point (0,3) satisfies this inequality. Show the necessary substitution.
(iii) The student now wishes the boundary to be included in the solution set while keeping the same shaded half-plane. Write the new inequality.
(iv) If another student, starting with the same boundary line, shades the half-plane that does not contain the origin, state the corresponding inequality and justify your answer.