Question

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

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

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