a) $y=\frac{3}{5} x-2$
Answer (1)
The equation is in slope-intercept form: y = m x + b .
Identify the slope: m = 5 3 .
Identify the y-intercept: b = − 2 .
The slope is 5 3 and the y-intercept is − 2 .
Explanation
Analyzing the Equation The given equation is y = 5 3 x − 2 . We need to analyze this linear equation, specifically identifying its slope and y-intercept.
Recognizing 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 By comparing the given equation y = 5 3 x − 2 with the slope-intercept form y = m x + b , we can identify the slope m as 5 3 .
Identifying the Y-Intercept Similarly, by comparing the given equation y = 5 3 x − 2 with the slope-intercept form y = m x + b , we can identify the y-intercept b as − 2 .
Conclusion Therefore, the slope of the line is 5 3 and the y-intercept is − 2 .
Examples
Understanding the slope and y-intercept of a line is crucial in many real-world applications. For instance, if you are tracking the distance a car travels over time, the slope represents the speed of the car, and the y-intercept could represent the initial distance from a starting point. Similarly, in business, a linear equation might represent the cost of producing items, where the slope is the cost per item, and the y-intercept is the fixed cost. Analyzing linear equations helps in making informed decisions and predictions in various fields.
