To find the slope of the line represented by the equation y = 2x + 3, we first need to understand that this equation is in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In our equation, y = 2x + 3, the coefficient of x is 2. Therefore, the slope of the line is 2. This means that for every unit increase in x, the value of y increases by 2.
Next, let’s create a table of x and y values for this equation. We can choose a few different values for x to see how y changes:
| x | y |
|---|---|
| -1 | 1 |
| 0 | 3 |
| 1 | 5 |
| 2 | 7 |
Now, let’s see how the slope is related to the entries in this table:
- For x = -1: y = 2(-1) + 3 = 1
- For x = 0: y = 2(0) + 3 = 3
- For x = 1: y = 2(1) + 3 = 5
- For x = 2: y = 2(2) + 3 = 7
As we can see from the calculations, when x increases by 1 (from -1 to 0, from 0 to 1, and from 1 to 2), the value of y increases by 2. This demonstrates the slope of the line being 2, confirming that the slope is indeed the rate of change of y with respect to x.