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Which of the following is true of the graph is in the -plane?
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Q. Which of the following is true of the graph is in the -plane?
- Rewrite Equation: Rewrite the equation in a more familiar form.To understand the graph of the equation , we can rewrite it in slope-intercept form (), where is the slope and is the y-intercept.Multiplying both sides by to get rid of the fraction, we get:
- Simplify Further: Simplify the equation further.We can simplify the slope by dividing both numerator and denominator by their greatest common divisor, which is .Now we have the slope-intercept form of the equation, where the slope is and the y-intercept is .
- Determine Slope: Determine the slope of the line.From the equation , we can see that the slope of the line is . This means that for every units the line moves horizontally to the right, it moves units vertically upwards.
- Determine Y-Intercept: Determine the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis. From the equation, we can see that the y-intercept is . This means the line crosses the y-axis at the point .
- Analyze Characteristics: Analyze the characteristics of the line.Based on the slope and y-intercept, we can say that the line is rising as it moves from left to right, and it crosses the y-axis at units above the origin. The line does not have any -intercept in the given equation, as it does not cross the -axis.
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