Asked by adaleta
Which of the following points is a solution to the linear inequality y>1/9x−2/9?(1 point)
Responses
(0,−1/9)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis
(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis
(0,−29)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis
(0,−13)
Responses
(0,−1/9)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis
(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis
(0,−29)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis
(0,−13)
Answers
Answered by
adaleta
Use the image to answer the question.
A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.
Is the point (0,−3) a solution to the inequality y>45x−3, as shown on the graph?
(1 point)
Responses
Yes, because (0,−3) falls within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
No, because (0,−3) falls within the shaded region.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
Yes, because (0,−3) falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3) falls on the boundary line.
A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.
Is the point (0,−3) a solution to the inequality y>45x−3, as shown on the graph?
(1 point)
Responses
Yes, because (0,−3) falls within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
No, because (0,−3) falls within the shaded region.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
Yes, because (0,−3) falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3) falls on the boundary line.
Answered by
GPT-4o mini
To determine which of the given points is a solution to the linear inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the x-value of each point into the inequality and check if the corresponding y-value satisfies it.
The inequality \( y > \frac{1}{9}x - \frac{2}{9} \) can be simplified for \( x = 0 \):
\[
y > \frac{1}{9}(0) - \frac{2}{9}
\]
\[
y > -\frac{2}{9}
\]
Now we can check each point:
1. **Point (0, -1/9)**:
\[
-\frac{1}{9} > -\frac{2}{9} \quad \text{(True)}
\]
2. **Point (0, -4/9)**:
\[
-\frac{4}{9} > -\frac{2}{9} \quad \text{(False)}
\]
3. **Point (0, -2/9)**:
\[
-\frac{2}{9} > -\frac{2}{9} \quad \text{(False)}
\]
4. **Point (0, -1/3)**:
\[
-\frac{1}{3} > -\frac{2}{9} \quad \text{(True since -1/3 is -3/9 and -3/9 > -2/9)}
\]
The only points that satisfy the inequality are (0, -1/9) and (0, -1/3).
Therefore, **the solution to the inequality is (0, -1/9)**.
The inequality \( y > \frac{1}{9}x - \frac{2}{9} \) can be simplified for \( x = 0 \):
\[
y > \frac{1}{9}(0) - \frac{2}{9}
\]
\[
y > -\frac{2}{9}
\]
Now we can check each point:
1. **Point (0, -1/9)**:
\[
-\frac{1}{9} > -\frac{2}{9} \quad \text{(True)}
\]
2. **Point (0, -4/9)**:
\[
-\frac{4}{9} > -\frac{2}{9} \quad \text{(False)}
\]
3. **Point (0, -2/9)**:
\[
-\frac{2}{9} > -\frac{2}{9} \quad \text{(False)}
\]
4. **Point (0, -1/3)**:
\[
-\frac{1}{3} > -\frac{2}{9} \quad \text{(True since -1/3 is -3/9 and -3/9 > -2/9)}
\]
The only points that satisfy the inequality are (0, -1/9) and (0, -1/3).
Therefore, **the solution to the inequality is (0, -1/9)**.
Answered by
GPT-4o mini
To determine whether the point \((0, -3)\) is a solution to the inequality \(y > 45x - 3\), we need to analyze the line represented by the equation and the shading on the graph.
1. **Boundary Line**: The equation is \(y = 45x - 3\), which is a straight line with a positive slope.
2. **Test the Point**: We substitute \(x = 0\) into the line equation:
\[
y = 45(0) - 3 = -3
\]
So, the point \((0, -3)\) lies exactly on the boundary line.
3. **Shading**: The shading extends from the line to the left, indicating that the points in the shaded area satisfy the inequality.
4. **Types of Inequality**: As this is a strict inequality \(y > 45x - 3\) (not including the equal part), points on the boundary line do not satisfy the inequality.
Given that (0, -3) is on the boundary line, it does not fall in the shaded area defined by \(y > 45x - 3\).
Therefore, the correct response is:
**No, because (0, -3) falls on the boundary line.**
1. **Boundary Line**: The equation is \(y = 45x - 3\), which is a straight line with a positive slope.
2. **Test the Point**: We substitute \(x = 0\) into the line equation:
\[
y = 45(0) - 3 = -3
\]
So, the point \((0, -3)\) lies exactly on the boundary line.
3. **Shading**: The shading extends from the line to the left, indicating that the points in the shaded area satisfy the inequality.
4. **Types of Inequality**: As this is a strict inequality \(y > 45x - 3\) (not including the equal part), points on the boundary line do not satisfy the inequality.
Given that (0, -3) is on the boundary line, it does not fall in the shaded area defined by \(y > 45x - 3\).
Therefore, the correct response is:
**No, because (0, -3) falls on the boundary line.**
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