Question

graph the equation
y=5/7x+2

x -10-10
y -10-10

Answer 1

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.