Asked by a
how to graph the inequality 2x-7y<-14
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To graph the inequality \( 2x - 7y < -14 \), follow these steps:
1. **Rewrite the inequality**: First, it's often helpful to express the inequality in slope-intercept form (i.e., \( y = mx + b \)). Start by isolating \( y \):
\[
2x - 7y < -14
\]
Subtract \( 2x \) from both sides:
\[
-7y < -2x - 14
\]
Now, divide every term by \(-7\). Remember that dividing or multiplying by a negative number reverses the inequality sign:
\[
y > \frac{2}{7}x + 2
\]
2. **Graph the boundary line**: The boundary line is given by the equation \( y = \frac{2}{7}x + 2 \). To graph this line, you can find two points:
- **Y-intercept**: Set \( x = 0 \):
\[
y = \frac{2}{7}(0) + 2 = 2
\]
This gives you the point \( (0, 2) \).
- **X-intercept**: Set \( y = 0 \):
\[
0 = \frac{2}{7}x + 2 \implies \frac{2}{7}x = -2 \implies x = -7
\]
This gives you the point \( (-7, 0) \).
Plot these points and draw a line through them. Since the inequality is \( y > \frac{2}{7}x + 2 \) and not \( y \geq \frac{2}{7}x + 2 \), the line should be dashed to indicate that points on the line are not included in the solution.
3. **Test a point**: To determine which side of the line to shade, choose a test point not on the line. A common choice is the origin \( (0, 0) \). Substitute \( (0, 0) \) into the original inequality:
\[
2(0) - 7(0) < -14 \implies 0 < -14
\]
This statement is false, so we do not shade the side of the line that includes the origin.
4. **Shade the correct area**: Since the inequality is \( y > \frac{2}{7}x + 2 \), you would shade the area above the dashed line.
Your final graph should show a dashed line representing \( y = \frac{2}{7}x + 2 \) with the area above the line shaded.
1. **Rewrite the inequality**: First, it's often helpful to express the inequality in slope-intercept form (i.e., \( y = mx + b \)). Start by isolating \( y \):
\[
2x - 7y < -14
\]
Subtract \( 2x \) from both sides:
\[
-7y < -2x - 14
\]
Now, divide every term by \(-7\). Remember that dividing or multiplying by a negative number reverses the inequality sign:
\[
y > \frac{2}{7}x + 2
\]
2. **Graph the boundary line**: The boundary line is given by the equation \( y = \frac{2}{7}x + 2 \). To graph this line, you can find two points:
- **Y-intercept**: Set \( x = 0 \):
\[
y = \frac{2}{7}(0) + 2 = 2
\]
This gives you the point \( (0, 2) \).
- **X-intercept**: Set \( y = 0 \):
\[
0 = \frac{2}{7}x + 2 \implies \frac{2}{7}x = -2 \implies x = -7
\]
This gives you the point \( (-7, 0) \).
Plot these points and draw a line through them. Since the inequality is \( y > \frac{2}{7}x + 2 \) and not \( y \geq \frac{2}{7}x + 2 \), the line should be dashed to indicate that points on the line are not included in the solution.
3. **Test a point**: To determine which side of the line to shade, choose a test point not on the line. A common choice is the origin \( (0, 0) \). Substitute \( (0, 0) \) into the original inequality:
\[
2(0) - 7(0) < -14 \implies 0 < -14
\]
This statement is false, so we do not shade the side of the line that includes the origin.
4. **Shade the correct area**: Since the inequality is \( y > \frac{2}{7}x + 2 \), you would shade the area above the dashed line.
Your final graph should show a dashed line representing \( y = \frac{2}{7}x + 2 \) with the area above the line shaded.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.