Question
Determine if the relation y=2x+6 is a function by graphing the relation and using the vertical line test. Is the relation a function?(1 point)
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GPT-4o mini
To determine if the relation \( y = 2x + 6 \) is a function, we can graph the equation and apply the vertical line test.
1. **Graphing the Equation**:
The equation \( y = 2x + 6 \) is in slope-intercept form ( \( y = mx + b \) ), where \( m = 2 \) is the slope and \( b = 6 \) is the y-intercept.
- The y-intercept is the point (0, 6).
- The slope of 2 means that for every 1 unit increase in \( x \), \( y \) increases by 2 units.
With these points, you can plot the line on a coordinate plane.
2. **Applying the Vertical Line Test**:
The vertical line test states that if a vertical line intersects the graph of a relation in more than one point, the relation is not a function.
Since \( y = 2x + 6 \) is a linear equation representing a straight line, any vertical line drawn on the graph will only intersect the line at one point.
Given that the line passes the vertical line test, we conclude that the relation \( y = 2x + 6 \) is indeed a function. Thus, the answer is **Yes, the relation is a function.**
1. **Graphing the Equation**:
The equation \( y = 2x + 6 \) is in slope-intercept form ( \( y = mx + b \) ), where \( m = 2 \) is the slope and \( b = 6 \) is the y-intercept.
- The y-intercept is the point (0, 6).
- The slope of 2 means that for every 1 unit increase in \( x \), \( y \) increases by 2 units.
With these points, you can plot the line on a coordinate plane.
2. **Applying the Vertical Line Test**:
The vertical line test states that if a vertical line intersects the graph of a relation in more than one point, the relation is not a function.
Since \( y = 2x + 6 \) is a linear equation representing a straight line, any vertical line drawn on the graph will only intersect the line at one point.
Given that the line passes the vertical line test, we conclude that the relation \( y = 2x + 6 \) is indeed a function. Thus, the answer is **Yes, the relation is a function.**