Pregunta
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Graph the line that passes through
24.

Ask by Todd Tyler. in the United States
Jan 27,2025

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To graph the line passing through with a slope of 2, use the equation . Plot the y-intercept at and another point like . Draw a straight line through these points to represent the line.

Solución

To graph the line that passes through the point with a slope , we can use the point-slope form of the equation of a line, which is given by:
where is a point on the line and is the slope.

Step 1: Substitute the known values

Here, and . Substituting these values into the equation gives:
This simplifies to:

Step 2: Simplify the equation

Now, we can simplify this equation:
Subtracting 2 from both sides:

Step 3: Graph the line

To graph the line :
  1. Identify the y-intercept: The y-intercept is (where the line crosses the y-axis).
  2. Use the slope: The slope means that for every 1 unit you move to the right (positive x-direction), you move up 2 units (positive y-direction).

Step 4: Plot points

  • Start at the y-intercept .
  • From there, move right 1 unit to and up 2 units to , giving the point .
  • You can also go left from the y-intercept: move left 1 unit to and down 2 units to , giving the point .

Final Graph

You can now draw a straight line through the points , , and to represent the line .
If you have graphing software or graph paper, you can plot these points and draw the line accordingly.

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Extra Insights

To graph the line that passes through the point with a slope , start at the point on the coordinate plane. From there, use the slope to find another point: since the slope is , for every unit you move to the right (the run), you move up units (the rise). This takes you from to . Plot the point and draw a straight line through both points, extending it in both directions.
A fun fact about lines is that every unique pair of points defines exactly one line. So if you have a different pair of points, don’t worry—you can always create a new graph! Just remember that the key elements are the points you start with and the slope, which tells you how steeply the line rises or falls. Get those coordinates plotted and watch your line come to life!

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