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graph the equation

y=5/7x+2

x -10-10
y -10-10

1 answer

To graph the equation \( y = \frac{5}{7}x + 2 \) within the given range for \( x \) and \( y \) from -10 to 10, follow these steps:

  1. Identify the slope and y-intercept:

    • The equation is in slope-intercept form \( y = mx + b \), where \( m = \frac{5}{7} \) and \( b = 2 \).
    • The y-intercept is \( (0, 2) \).

  2. Find additional points:

    • Choose x-values to find corresponding y-values. Using a few values in the range of -10 to 10:
      • For \( x = -10 \): \[ y = \frac{5}{7}(-10) + 2 = -\frac{50}{7} + 2 \approx -5.14 \]
      • For \( x = 0 \): \[ y = 2 \]
      • For \( x = 10 \): \[ y = \frac{5}{7}(10) + 2 = \frac{50}{7} + 2 \approx 9.14 \]
    • The points are:
      • \( (-10, -5.14) \)
      • \( (0, 2) \)
      • \( (10, 9.14) \)

  3. Plot the points:

    • Plot the points \( (-10, -5.14) \), \( (0, 2) \), and \( (10, 9.14) \) on a coordinate plane.

  4. Draw the line:

    • Connect the points with a straight line that extends through the graph.

Summary of Coordinates:

  • Points to plot:
    • \( (-10, -5.14) \)
    • \( (0, 2) \)
    • \( (10, 9.14) \)

Here's a simple text representation of the graph:

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

Make sure your graph matches this information and includes the line representing the equation. Adjust for accuracy in an actual graphing tool or on graph paper.