UpStudy Free Solution:

1. Identify Two Points:

Select two points on the line. For example, if you have points \(( x_ 1, y_ 1) \) and \(( x_ 2, y_ 2) \).

2. Calculate Vertical Change (\(\Delta y\)):

\[\Delta y = y_ 2 - y_ 1\]

3. Calculate Horizontal Change (\(\Delta x\)):

\[\Delta x = x_ 2 - x_ 1\]

4. Compute Slope:

Substitute these values into the slope formula:

\[m = \frac { \Delta y} { \Delta x} \]

For example, if we have points (0, 0) and (3, 9):

- Vertical change: \(9 - 0 = 9\)

- Horizontal change: \(3 - 0 = 3\)

- Slope: \(m = \frac { 9} { 3} = 3\)

Supplemental Knowledge

The slope of a line measures its steepness and is calculated as the ratio of the vertical change (\(\Delta y\)) to the horizontal change (\(\Delta x\)) between two points on the line. The formula for the slope \(m\) is:
\[m = \frac { \Delta y} { \Delta x} = \frac { y_ 2 - y_ 1} { x_ 2 - x_ 1} \]
where \(( x_ 1, y_ 1) \) and \(( x_ 2, y_ 2) \) are two distinct points on the line.

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