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Two Points: Find Slope and Intercept.

Given two points,

$p_1 = (x_1, y_1)$

$p_2 = (x_2, y_2)$ For the line passing through these two points, find the:

slope, and
intercept

Fig 1. Two points. Point 1: (1, 2) and Point2: (5, 4).

Notes and Code Outcome

Notes and Code	Outcome
Slope The slope of the line is the change in y divided by the change in x: $\text{slope} = \frac{\Delta y}{\Delta x}$ For two points, the change in y and change in x are: $\Delta y = y_2 - y_1$ $\Delta x = x_2 - x_1$	⇨ The output of your program should be something like: `The slope is: 0.5`
Intercept Finding the intercept requires a little algebra. Since the general equation for a straight line is: $y = mx+b$ where: $m = \text{slope}$ $b = \text{intercept}$ so to find the intercept we solve this equation for b: $y - mx = b$ therefore, $b = y - mx$ since we already calculated the slope (m), and we know the x and y values of at least one point, we can substitute in the values: $x = x_1$ $y = y_1$ to get: $b = y_1 - m x_1$	⇨ The output of your program should be something like: `The slope is: 0.5 The intercept is: 1.5`
Exercise: Draw a graph showing the two points and the line between them, then extend the line to the boundaries of your graph.

Slope

The slope of the line is the change in y divided by the change in x:

$\text{slope} = \frac{\Delta y}{\Delta x}$

For two points, the change in y and change in x are:

$\Delta y = y_2 - y_1$

$\Delta x = x_2 - x_1$

⇨

# INPUT
#   Set the two points
(x1, y1) = (1, 2)
(x2, y2) = (5, 4)

# CALCULATIONS
#   calculate the changes in x and y
dx = x2 - x1
dy = y2 - y1

#   calculate the slope
slope = dy / dx

#OUTPUT
print("The slope is:", slope)

The output of your program should be something like:

The slope is: 0.5

Intercept

Finding the intercept requires a little algebra. Since the general equation for a straight line is:

$y = mx+b$ where:

$m = \text{slope}$

$b = \text{intercept}$ so to find the intercept we solve this equation for b:

$y - mx = b$ therefore,

$b = y - mx$ since we already calculated the slope (m), and we know the x and y values of at least one point, we can substitute in the values:

$x = x_1$

$y = y_1$ to get:

$b = y_1 - m x_1$

⇨

# INPUT
#   Set the two points
(x1, y1) = (1, 2)
(x2, y2) = (5, 4)

# CALCULATIONS
#   calculate the changes in x and y
dx = x2 - x1
dy = y2 - y1

#   calculate the slope
slope = dy / dx

#   calculate the intercept
intercept = y1 - slope * x1

#OUTPUT
print("The slope is:", slope)
print("The intercept is:", intercept)

The output of your program should be something like:

The slope is: 0.5
The intercept is: 1.5

Exercise: Draw a graph showing the two points and the line between them, then extend the line to the boundaries of your graph.