To find the slope of a linear function represented in a table of values, you need to identify two points from the table. Each point will be in the form of (x, y), where ‘x’ is the input value and ‘y’ is the output value. The slope (m) of a linear function is calculated using the formula:
m = (y2 – y1) / (x2 – x1)
Where:
- (x1, y1) and (x2, y2) are two points from the table.
Here’s a step-by-step method to find the slope:
- Select two points: Look at your table and pick any two points. For instance, if your table has points (2, 3) and (4, 7), then:
- Identify the coordinates: Let (2, 3) be (x1, y1) and (4, 7) be (x2, y2).
- Subtract the y-values: Calculate y2 – y1: 7 – 3 = 4.
- Subtract the x-values: Calculate x2 – x1: 4 – 2 = 2.
- Calculate the slope: Divide the difference in y-values by the difference in x-values: m = (7 – 3) / (4 – 2) = 4 / 2 = 2.
So, the slope of the function represented by the table is 2. This means for every 1 unit increase in x, the value of y increases by 2 units. In a graphical representation, this slope indicates how steeply the line rises or falls.
Remember, a positive slope indicates that the function is increasing, while a negative slope indicates a decreasing function. If the slope is zero, the line is horizontal, indicating that y remains constant as x changes.
Now you can confidently determine the slope from any table of values representing a linear function!