Solve the given inequality graphically in a two-dimensional plane: $-3x + 2y \geq -6$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The graphical representation of the line $-3x + 2y = -6$ is shown in the figure.
This line divides the $xy$-plane into two half-planes.
To determine the solution region,we select a test point not on the line,such as $(0, 0)$.
Substituting $(0, 0)$ into the inequality:
$-3(0) + 2(0) \geq -6$
$0 \geq -6$,which is a true statement.
Since the point $(0, 0)$ satisfies the inequality,the solution region is the half-plane containing the origin $(0, 0)$.
Because the inequality is $\geq$,the line itself is included in the solution region. The shaded region in the figure represents the solution set.

Explore More

Similar Questions

Solve $\frac{3x-4}{2} \geq \frac{x+1}{4}-1$. Show the graph of the solutions on a number line.

Solve the given inequality graphically in a two-dimensional plane: $y+8 \geq 2x$

Solve the following inequality graphically in a two-dimensional plane: $2x + y > 3$.

Solve the inequality $2 \leq 3x - 4 \leq 5$.

Out of the following points,how many points satisfy the inequality $2x - 3y > -5$?
$(1, 1), (-1, 1), (1, -1), (-1, -1), (-2, 1), (2, -1), (-1, 2)$ and $(-2, -1)$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo