How do you find the slope of the line y = 5x - 2?

The slope of the line \( y = 5x - 2 \) is 5.

To find the slope of a line given its equation in the form \( y = mx + c \), you need to identify the coefficient of \( x \). This form is known as the slope-intercept form, where \( m \) represents the slope and \( c \) represents the y-intercept. In the equation \( y = 5x - 2 \), the coefficient of \( x \) is 5. Therefore, the slope of the line is 5.

The slope of a line indicates how steep the line is and the direction it goes. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls. In this case, since the slope is 5, the line rises steeply as you move from left to right. The larger the value of the slope, the steeper the line.

Understanding the slope is crucial in many areas of mathematics and real-life applications, such as calculating rates of change, understanding trends in data, and solving problems involving linear relationships. For example, if you were analysing the speed of a car over time, the slope of the line on a graph would tell you how quickly the car is accelerating or decelerating.