How Do You Understand Slopes and Calculate Overlapping Areas?

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Understanding slopes involves using the slope formula, which requires plugging in specific coordinates to determine the slope of a line. For a triangle defined by points on the x-axis at -2 and 2, converging at a height of 2 on the y-axis, visualizing the shape is crucial for calculating overlapping areas. To find the area of overlap between a rectangle and the triangle, one must first identify the dimensions of the overlapping region rather than simply multiplying the heights of the two shapes. Drawing a diagram can help clarify the overlapping figure and facilitate accurate area calculations. Clear visualization and understanding of the shapes involved are essential for solving these types of problems.
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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.
 
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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.
 
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