Question
Graph the inequality on the axes below.
y, is less than, 3, x, minus, 7
y<3x−7
y, is less than, 3, x, minus, 7
y<3x−7
Answers
Answer
and whats the slope
Answered by
GPT-4o mini
To graph the inequality \( y < 3x - 7 \), follow these steps:
1. **Graph the Boundary Line**: First, graph the equation of the line \( y = 3x - 7 \). This line acts as the boundary for the inequality. Since the inequality is strict (\(<\)), you will draw a dashed line to indicate that points on the line are not included in the solution.
- To do this:
- Find the y-intercept (where \( x = 0 \)):
\[
y = 3(0) - 7 = -7 \, (0, -7)
\]
- Find another point. For example, let \( x = 1 \):
\[
y = 3(1) - 7 = 3 - 7 = -4 \, (1, -4)
\]
- Plot these points on the graph and draw a dashed line through them.
2. **Shade the Region**: Since the inequality is \( y < 3x - 7 \), you need to shade the area below the line. This represents all the points where the y-value is less than the expression \( 3x - 7 \).
### Summary of Graph:
- A dashed line representing \( y = 3x - 7 \).
- Shade the region below the dashed line.
Ensure to label the axes and the boundary line to clarify your graph! If you have graph paper, you can use it to make your graph more precise.
1. **Graph the Boundary Line**: First, graph the equation of the line \( y = 3x - 7 \). This line acts as the boundary for the inequality. Since the inequality is strict (\(<\)), you will draw a dashed line to indicate that points on the line are not included in the solution.
- To do this:
- Find the y-intercept (where \( x = 0 \)):
\[
y = 3(0) - 7 = -7 \, (0, -7)
\]
- Find another point. For example, let \( x = 1 \):
\[
y = 3(1) - 7 = 3 - 7 = -4 \, (1, -4)
\]
- Plot these points on the graph and draw a dashed line through them.
2. **Shade the Region**: Since the inequality is \( y < 3x - 7 \), you need to shade the area below the line. This represents all the points where the y-value is less than the expression \( 3x - 7 \).
### Summary of Graph:
- A dashed line representing \( y = 3x - 7 \).
- Shade the region below the dashed line.
Ensure to label the axes and the boundary line to clarify your graph! If you have graph paper, you can use it to make your graph more precise.
Answered by
GPT-4o mini
The slope of the linear equation \(y = 3x - 7\) can be determined from its slope-intercept form, which is:
\[
y = mx + b
\]
where:
- \(m\) is the slope,
- \(b\) is the y-intercept.
In the equation \(y = 3x - 7\):
- The slope \(m\) is \(3\).
- The y-intercept \(b\) is \(-7\) (the point where the line crosses the y-axis).
### Slope Interpretation:
- A slope of \(3\) means that for every 1 unit increase in \(x\), \(y\) increases by \(3\) units. Graphically, this indicates the steepness and direction of the line—because the slope is positive, the line rises from left to right.
\[
y = mx + b
\]
where:
- \(m\) is the slope,
- \(b\) is the y-intercept.
In the equation \(y = 3x - 7\):
- The slope \(m\) is \(3\).
- The y-intercept \(b\) is \(-7\) (the point where the line crosses the y-axis).
### Slope Interpretation:
- A slope of \(3\) means that for every 1 unit increase in \(x\), \(y\) increases by \(3\) units. Graphically, this indicates the steepness and direction of the line—because the slope is positive, the line rises from left to right.
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