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 (1)
The equation is in the form y = m x + b , where m is the slope.
Comparing y = − 2 1 x + 4 1 with y = m x + b , we identify m = − 2 1 .
The slope of the line is − 2 1 .
Explanation
Understanding the equation The equation of the line is given as y = − 2 1 x + 4 1 . We need to find the slope of this line.
Recalling slope-intercept form The equation is in slope-intercept form, which is y = m x + b , where m represents the slope 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. In this case, m = − 2 1 .
Stating the slope Therefore, the slope of the line is − 2 1 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, if you're analyzing the steepness of a hill on a map, the slope tells you how much the elevation changes for every unit of horizontal distance. Similarly, in finance, the slope of a trend line on a stock chart can indicate the rate at which the stock price is increasing or decreasing, helping investors make informed decisions. Knowing how to find the slope from an equation allows you to quickly understand the rate of change in various scenarios.
