What is the slope of the line represented by the equation $y=-\frac{2}{3}-5 x$?
A. -5
B. $-\frac{2}{3}$
C. $\frac{2}{3}$
D. 5
Answer (2)
Rewrite the given equation y = − 3 2 − 5 x in slope-intercept form.
Identify the coefficient of x in the slope-intercept form, which represents the slope of the line.
The equation in slope-intercept form is y = − 5 x − 3 2 .
The slope of the line is − 5 .
Explanation
Understanding the Problem We are given the equation of a line: y = − 3 2 − 5 x . Our goal is to identify the slope of this line. To do this, we will rewrite the equation in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept.
Rewriting the Equation Let's rewrite the given equation to match the slope-intercept form. We have y = − 5 x − 3 2 .
Identifying the Slope By comparing the rewritten equation y = − 5 x − 3 2 with the slope-intercept form y = m x + b , we can see that the coefficient of x is − 5 . Therefore, the slope of the line is − 5 .
Final Answer The slope of the line represented by the equation y = − 3 2 − 5 x is − 5 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For instance, 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 economics, the slope of a cost function can represent the marginal cost, indicating how much the cost increases for each additional unit produced. Linear relationships are everywhere, and the slope is a key parameter to understand them.
The slope of the line represented by the equation y = − 3 2 − 5 x is − 5 . Thus, the correct choice is A. -5.
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