What is the slope of the line represented by the equation $y=-\frac{1}{2} x+\frac{1}{4}$?
A. $-\frac{1}{2}$
B. $-\frac{1}{4}$
C. $\frac{1}{4}$
D. $\frac{1}{2}$
Answer (2)
The equation is already in slope-intercept form: y = m x + b .
Identify the slope m as the coefficient of x .
In the equation y = − 2 1 x + 4 1 , the slope m is − 2 1 .
Therefore, the slope of the line is − 2 1 .
Explanation
Understanding the equation The given equation is y = − 2 1 x + 4 1 . We need to find the slope of the line represented by this equation.
Recalling slope-intercept form The slope-intercept form of a linear equation is given by y = m x + b , where m represents the slope of the line and b represents the y-intercept.
Identifying the slope Comparing the given equation y = − 2 1 x + 4 1 with the slope-intercept form y = m x + b , we can identify the coefficient of x as the slope m . In this case, m = − 2 1 .
Stating the final answer Therefore, the slope of the line represented by the equation y = − 2 1 x + 4 1 is − 2 1 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, in construction, the slope of a ramp determines its steepness, affecting accessibility. In economics, the slope of a supply or demand curve indicates how sensitive the quantity is to changes in price. In physics, the slope of a velocity-time graph represents acceleration. Knowing the slope helps in making informed decisions and predictions in various fields.
The slope of the line represented by the equation y = − 2 1 x + 4 1 is − 2 1 , which is option A. This slope indicates a downward trend as x increases. It signifies that for each unit increase in x, y decreases by half a unit.
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