Question 1
Which line has a slope of -68.7 and a $y$-intercept of -5.1 ?
$y=-5.1 x-68.7 \quad y=-68.7 x-5.1$
$y=-5.1 x+68.7$
$y=68.7 x-5.1$
Answer (1)
The equation of a line is given by y = m x + b , where m is the slope and b is the y -intercept. Given m = − 68.7 and b = − 5.1 , we substitute these values into the equation to find the equation of the line. The equation of the line is y = − 68.7 x − 5.1 .
Explanation
Understanding the Problem We are given the slope m = − 68.7 and the y -intercept b = − 5.1 . The equation of a line is given by y = m x + b . We need to find the equation of the line with the given slope and y -intercept.
Finding the Equation Substitute the given values of the slope and y -intercept into the equation y = m x + b . We have m = − 68.7 and b = − 5.1 . Therefore, the equation of the line is y = − 68.7 x − 5.1 .
Final Answer The equation of the line with a slope of -68.7 and a y -intercept of -5.1 is y = − 68.7 x − 5.1 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For instance, if you are tracking the depreciation of a car's value over time, you can use a linear equation where the slope represents the rate of depreciation and the y-intercept represents the initial value of the car. Similarly, in business, linear equations can model the relationship between production costs and the number of items produced, helping to predict expenses and profits. This concept extends to physics, where linear relationships describe motion at a constant speed, and in everyday budgeting, where you can track your savings or spending habits.
