Graph the line with the equation y, equals, start fraction, 2, divided by, 5, end fraction, x, plus, 3y=

Question

5
2
​
x+3.

Answer 1

To graph the line given by the equation \( y = \frac{2}{5}x + 3 \), let's first identify key elements of the equation and then draw the graph.

1. Identify the slope and y-intercept:

   • The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.
   • Here, the slope \( m = \frac{2}{5} \) and the y-intercept \( b = 3 \).

2. Plot the y-intercept:

   • Start by placing a point at \( (0, 3) \) on the y-axis.

3. Use the slope to find another point:

   • From the point \( (0, 3) \), use the slope \( \frac{2}{5} \). This means for every 5 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
   • From \( (0, 3) \), move right 5 units to \( x = 5 \) and then up 2 units to \( y = 5 \). This gives you another point: \( (5, 5) \).

4. Draw the line:

   • With the points \( (0, 3) \) and \( (5, 5) \) plotted, draw a straight line through these points, extending it in both directions.

5. Optional - Finding another point:

   • You can find another point by choosing a negative x-value. For example, let \( x = -5 \): \[ y = \frac{2}{5}(-5) + 3 = -2 + 3 = 1. \] So the point \( (-5, 1) \) can also be plotted to further confirm the line.

The graph of the line will look like this:

 |
6|                 * (5,5)
5|              * 
4|              
3|      * (0,3)
2|    
1|  * (-5,1)
0|____________________
    -5  0  5  10

This line represents the equation \( y = \frac{2}{5}x + 3 \).