Finding the slope-intercept form (y = mx + b) of a linear equation from a table involves determining the slope (m) and the y-intercept (b) using the data provided. Here's a step-by-step guide:
1. Understanding Slope-Intercept Form
The slope-intercept form of a linear equation is represented as:
- y = mx + b
Where:
- 'y' represents the dependent variable.
- 'x' represents the independent variable.
- 'm' represents the slope of the line.
- 'b' represents the y-intercept (the point where the line crosses the y-axis).
2. Calculating the Slope (m)
The slope (m) indicates the rate of change of 'y' with respect to 'x'. You can calculate it using any two points from the table: (x₁, y₁) and (x₂, y₂).
- m = (y₂ - y₁) / (x₂ - x₁)
This formula calculates the "rise over run."
Example:
Suppose your table has the following points:
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
Using points (1, 2) and (2, 4):
- m = (4 - 2) / (2 - 1) = 2 / 1 = 2
Therefore, the slope (m) is 2.
3. Determining the Y-Intercept (b)
Once you have the slope (m), you can find the y-intercept (b) by substituting the slope and the coordinates of any point from the table into the slope-intercept equation (y = mx + b) and solving for 'b'.
Example (Continuing from above):
We know m = 2. Let's use the point (1, 2).
- y = mx + b
- 2 = 2(1) + b
- 2 = 2 + b
- b = 0
Therefore, the y-intercept (b) is 0.
4. Writing the Slope-Intercept Equation
Now that you have both the slope (m) and the y-intercept (b), plug these values back into the slope-intercept form (y = mx + b).
Example (Continuing from above):
- m = 2
- b = 0
The equation is:
- y = 2x + 0 or simply y = 2x
Summary
To find the slope-intercept form from a table:
- Calculate the slope (m) using two points from the table.
- Substitute the slope (m) and one point from the table into y = mx + b.
- Solve for the y-intercept (b).
- Write the equation using the values of m and b.
