Question

how to graph the inequality 2x-7y<-14, give coordinates

Answer 1

To graph the inequality \( 2x - 7y < -14 \), you can follow these steps:

1. **Convert the inequality to an equation**: Start by turning the inequality into an equation to find the boundary line. Set \( 2x - 7y = -14 \).

2. **Find intercepts**: This is helpful for graphing the line.
- **x-intercept**: Set \( y = 0 \) and solve for \( x \):
\[
2x - 7(0) = -14 \implies 2x = -14 \implies x = -7.
\]
So, the x-intercept is \((-7, 0)\).
- **y-intercept**: Set \( x = 0 \) and solve for \( y \):
\[
2(0) - 7y = -14 \implies -7y = -14 \implies y = 2.
\]
So, the y-intercept is \((0, 2)\).

3. **Plot the line**: Draw the line that passes through the points \((-7, 0)\) and \((0, 2)\). Since the inequality is \( < \), you will use a dashed line to indicate that points on the line are not included in the solution.

4. **Test a point**: To determine which side of the line to shade, choose a test point that is not on the line. The point \((0, 0)\) is a good choice:
\[
2(0) - 7(0) < -14 \implies 0 < -14.
\]
This inequality is false, so we do not shade the region that includes \((0, 0)\). Instead, we shade the opposite side of the line.

5. **Final shading**: Shade the region of the graph that is below the dashed line, as this represents all the points that satisfy the inequality \( 2x - 7y < -14 \).

### Coordinates:
- X-intercept: \((-7, 0)\)
- Y-intercept: \((0, 2)\)
- Test point: \((0, 0)\)

These steps will help you accurately graph the inequality \( 2x - 7y < -14 \) on a coordinate plane.