Which line has a slope of -68.7 and a $y$-intercept of -5.1?
A. $y=68.7 x-5.1$
B. $y=-5.1 x-68.7$
C. $y=-68.7 x-5.1$
D. $y=-5.1 x+68.7$
Answer (1)
The slope-intercept form of a line is y = m x + b , where m is the slope and b is the y -intercept.
We are given m = − 68.7 and b = − 5.1 .
Substituting these values into the equation, we get y = − 68.7 x − 5.1 .
Therefore, the equation of the line is y = − 68.7 x − 5.1 .
Explanation
Understanding the Problem We are given the slope and y -intercept of a line and asked to find the equation of the line. The slope-intercept form of a line is given by y = m x + b , where m is the slope and b is the y -intercept. In this problem, we are given that the slope is m = − 68.7 and the y -intercept is b = − 5.1 .
Finding the Equation We substitute the given values of m and b into the slope-intercept form of the equation of a line, y = m x + b . Substituting m = − 68.7 and b = − 5.1 , we get y = − 68.7 x − 5.1 .
Final Answer The equation of the line with slope -68.7 and y -intercept -5.1 is y = − 68.7 x − 5.1 . Comparing this to the given options, we see that the correct answer is y = − 68.7 x − 5.1 .
Examples
Understanding the slope and y-intercept of a line is crucial in many real-world applications. For example, if you are tracking the depreciation of a car, the slope represents the rate at which the car's value decreases each year, and the y-intercept represents the initial value of the car. Similarly, in business, the slope can represent the rate of profit or loss, and the y-intercept can represent the initial investment.
