DS Slope and Intercept

Slope and Intercept

Here’s how we determine the slope and intercept of our function:

f(x) = 2x + 80

The image below highlights the Slope, which represents the steepness of the line, and the Intercept, which is the y-value when x = 0 (the point where the diagonal line intersects the vertical axis). The red line extends the blue line from the previous page.

img_linearity5

Find The Slope

The slope represents how much calorie burnage increases when the average pulse increases by one. It indicates the “steepness” of the diagonal line.

The slope can be calculated using the proportional difference between two points on the graph:

When the average pulse is 80, the calorie burnage is 240.
When the average pulse is 90, the calorie burnage is 260.

This shows that for every 10-unit increase in average pulse, calorie burnage increases by 20.

Slope = 20/10 = 2

The slope equals 2.

Mathematically, the slope is defined as:

Slope = f(x2) – f(x1) / x2-x1

$f (x_{2})$ : Second value of Calorie_Burnage = 260
$f(x_1)$ : First value of Calorie_Burnage = 240
$x_2$ : Second value of Average_Pulse = 90
$x_1$ : First value of Average_Pulse = 80

Slope = (260-240) / (90 – 80) = 2

Use Python to Find the Slope

Use the following code to calculate the slope:

Example

def slope(x1, y1, x2, y2):
s = (y2-y1)/(x2-x1)
return s

print (slope(80,240,90,260))