Question

graph the equation y+3=2(x+3)?

Answer 1

First rewrite in slope-intercept form:

y + 3 = 2(x + 3)
y + 3 = 2x + 6
y = 2x + 3

So the line has slope m = 2 and y-intercept b = 3.

How to graph it:
- Plot the y-intercept: (0, 3).
- Use the slope rise/run = 2/1: from (0,3) go up 2 and right 1 to get (1,5). Repeat to get more points, or go left 1 and down 2 to (−1,1).
- You can also get the x-intercept by setting y = 0: 0 = 2x + 3 → x = −3/2 = −1.5 (point (−1.5, 0)).
- Draw a straight line through the plotted points.

Example points to plot: (−1.5, 0), (−1, 1), (0, 3), (1, 5).

If you want a quick plot in Python (matplotlib), run:
```
import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-4, 4, 101)
y = 2*x + 3
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.plot(x, y, '-b')
plt.scatter([0, 1, -1.5], [3, 5, 0], color='red') # example points
plt.gca().set_aspect('equal', adjustable='box')
plt.grid(True)
plt.show()
```