Finding slope from a graph.
Understand the Problem
The image provides information on how to find the slope from a graph, including definitions and formulas related to slope calculation.
Answer
The slope \( m \) is \( 1 \).
Answer for screen readers
The slope ( m ) is ( 1 ).
Steps to Solve
- Identify the coordinates of the two points on the graph
From the graph, we can identify two points where the line crosses the grid. Let's say these points are ( A(2, 3) ) and ( B(5, 6) ).
- Calculate the rise
The rise is the change in the y-coordinates of the two points.
Using the formula: $$ \text{rise} = y_2 - y_1 $$ For points ( A(2, 3) ) and ( B(5, 6) ): $$ \text{rise} = 6 - 3 = 3 $$
- Calculate the run
The run is the change in the x-coordinates of the two points.
Using the formula: $$ \text{run} = x_2 - x_1 $$ For points ( A(2, 3) ) and ( B(5, 6) ): $$ \text{run} = 5 - 2 = 3 $$
- Calculate the slope
Substituting the rise and run into the slope formula: $$ m = \frac{\text{rise}}{\text{run}} $$ $$ m = \frac{3}{3} = 1 $$
- Simplify the slope
Since ( \frac{3}{3} = 1 ), the slope ( m ) can be expressed simply as 1. The slope indicates that for every unit increase in ( x ), ( y ) also increases by 1.
The slope ( m ) is ( 1 ).
More Information
A slope of 1 means that the line rises at a 45-degree angle from the left to the right, which indicates a consistent relationship between the x and y values.
Tips
- Confusing rise and run can lead to incorrect slope calculation. Ensure you correctly identify which is which.
- Failing to reduce the fraction can lead to a misconception about the slope's value. Always simplify if possible.
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