Identify the slope.
Understand the Problem
The question is asking to determine the slope of a line shown in a graph. To solve this, we will analyze the coordinates of two points on the line and apply the slope formula.
Answer
The slope is $m = 1$.
Answer for screen readers
The slope of the line is $m = 1$.
Steps to Solve
- Identify two points on the line
From the graph, we can identify two points on the line. Let's use the points (2, 4) and (0, 2).
- Use the slope formula
The slope $m$ of a line is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Substituting our points into the formula:
- Let point 1 be $(x_1, y_1) = (2, 4)$
- Let point 2 be $(x_2, y_2) = (0, 2)$
- Calculate the differences
Now we will calculate the differences in the coordinates:
- $y_2 - y_1 = 2 - 4 = -2$
- $x_2 - x_1 = 0 - 2 = -2$
- Plug in the values into the slope formula
Substituting the differences into the slope formula gives:
$$ m = \frac{-2}{-2} $$
- Simplify the result
Simplifying the fraction results in:
$$ m = 1 $$
The slope of the line is $m = 1$.
More Information
The slope of a line represents the rate of change of $y$ with respect to $x$. A slope of $1$ indicates that for every unit increase in $x$, $y$ increases by 1 unit as well. This means the line rises diagonally at a 45-degree angle.
Tips
- Incorrectly identifying points: Ensure you choose points that lie exactly on the line.
- Confusing the signs: Pay attention to negative and positive values, particularly when calculating the differences.
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