Trouble understanding slopes

[skan]

I am having troubel understanding slopes. I know the slope formulas but when given a triangle function, say on the x-axis one end of the base of the triangle is at -2 and the other end at 2 and on the y-axis they converge at 2.

and given a rect function, and when asked to find the area of overlap between the rect and triangle function, I multiply the amplitude or height of the rect function with what of the triangle function?

thanks a lot.

 

[Gokul43201]

1. What is the slope formula ? You just have to plug in the numbers to find the slopes.

2. No, you draw a picture and figure out the shape of the overlapping figure. Find out the dimensions of this shape and calculate its area.

 

[tacman]

Understanding slopes can be challenging at first, but with practice and a clear understanding of the concepts, it can become easier. The slope of a line is a measure of its steepness and is represented by the ratio of the change in y-values to the change in x-values. In your example, the triangle function can be represented by two points (-2, 0) and (2, 2) on the x-y plane. To find the slope of this line, you can use the slope formula: (y2-y1)/(x2-x1). In this case, it would be (2-0)/(2-(-2)) = 1/2. This means that for every 1 unit increase in the x-value, there is a 1/2 unit increase in the y-value.

When finding the area of overlap between the rect and triangle function, you can use the height of the rect function and multiply it by the base of the triangle function. In your example, the height of the rect function would be 2 and the base of the triangle function would be 4 (since the distance between -2 and 2 on the x-axis is 4 units). So, the area of overlap would be 2*4 = 8 square units.

Remember, the slope is just a measure of the steepness of a line and can be calculated using the slope formula. And when finding the area of overlap between two functions, you can use the height of one function and multiply it by the base of the other function. I hope this helps clarify your understanding of slopes. Keep practicing and seeking out resources for further understanding. Good luck!