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graph the equation y=5/6 x + 1

10 to -10 is x
10 to -10 is y

1 answer

To graph the equation \( y = \frac{5}{6}x + 1 \), follow these steps:

  1. Identify the Y-Intercept: The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The y-intercept here is \( 1 \) (where the line crosses the y-axis).

  2. Calculate the Slope: The slope \( \frac{5}{6} \) means that for every increase of \( 6 \) in \( x \), \( y \) increases by \( 5 \). This can help us plot additional points.

  3. Plot Points:

    • Start by plotting the y-intercept (0, 1).
    • Use the slope to find another point. From (0, 1):
      • Move 6 units to the right (increase \( x \) by \( 6 \)), and move 5 units up (increase \( y \) by \( 5 \)) to get the point (6, 6).
    • Alternatively, you can move in the opposite direction: from (0, 1), move 6 units to the left (decrease \( x \) by \( 6 \)), and move 5 units down (decrease \( y \) by \( 5 \)) to get the point (-6, -4).

  4. Draw the Line: Connect the points (0, 1), (6, 6), and (-6, -4) with a straight line and extend it to cover the range \( -10 \) to \( 10 \) on both axes.

  5. Set the Axes: Ensure your graph has:

    • X-axis ranging from \( -10 \) to \( 10 \).
    • Y-axis ranging from \( -10 \) to \( 10 \).

Here is a rough sketch of how the graph will look:

 y
10 |                              
   |                      
 6 |                   *
   |
 5 |
   |
 4 |
   |
 3 |
   |
 2 |               *        
   |
 1 | *             
   |---------------------------------- x
   -10     -6     0     6     10
   |
 -1 |
   |
 -4 |          *
   |
 -5 |
   |
 -6 |
   |
 -7 |
   |
 -8 |
   |
 -9 |
  -10 |

In the above sketch, the points plotted correspond to the calculated coordinates. The line goes through the y-intercept at (0, 1), continues upwards through (6, 6), and downwards through (-6, -4). Adjust the scale as needed for a more accurate representation.