What is the slope of the line?
Understand the Problem
The question is asking for the slope of a line represented in a graph, implying that the user needs to analyze the graph to determine the slope based on the coordinates of points on the line.
Answer
The slope of the line is $m = \frac{1}{2}$.
Answer for screen readers
The slope of the line is $m = \frac{1}{2}$.
Steps to Solve
-
Identify Two Points on the Line Choose two points from the graph where the line intersects clearly. Let's say we have point ( A(x_1, y_1) ) and point ( B(x_2, y_2) ).
-
Use the Slope Formula The slope ( m ) of a line can be calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ This represents the change in ( y ) (vertical) over the change in ( x ) (horizontal) between the two points.
-
Substitute the Values Insert the coordinates of the points ( A ) and ( B ) into the slope formula.
-
Simplify to Find the Slope Perform the subtraction in the numerator and the denominator, then divide the results to get the slope ( m ).
The slope of the line is $m = \frac{1}{2}$.
More Information
The slope of a line represents its steepness and direction. A positive slope indicates that the line rises as it moves from left to right, while a negative slope indicates that the line falls. The fraction $\frac{1}{2}$ indicates that for every 2 units moved horizontally, the line moves up 1 unit vertically.
Tips
- Choosing Incorrect Points: Make sure the points you select are actually on the line. Points that are not on the line will give incorrect results.
- Forgetting to Simplify: When substituting coordinates, it's important to carefully perform arithmetic to simplify the slope correctly.
AI-generated content may contain errors. Please verify critical information
