Learning about finding the slope of a line

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In summary, understanding the concept of slope is crucial in learning about finding the slope of a line. It is determined by dividing the change in y-coordinate by the change in x-coordinate. This concept applies to both algebra and graphing, where the slope can be measured using rise over run. The slope can also be represented as an angle using the arctan function.
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A day or so ago you hadn't any idea what a slope was and now you're asking about dy/dx? How about just taking it slowly and actually LEARNING each topic well before going on to the next?

(I notice that after not understanding the responses you got on this board, you complained that your teacher was "not good at explanations". I see a tendency to jump at ideas then complain about any explanation that does not verify your preconceptions.)

In any case, dy/dx has nothing to do with "infinite slopes". A straight line has a fixed slope (another way to calculate the slope it to take the tangent of the of the angle the line makes with any horizontal line). A curve does not have a "slope" but we can draw a tangent line to the curve and find its slope. That is dy/dx.
 
<h2> What is the definition of slope?</h2><p>Slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-values of two points on the line by the change in the x-values of those same points.</p><h2> How do you find the slope of a line?</h2><p>To find the slope of a line, you need to have two points on the line. Then, you can use the slope formula: (y<sub>2</sub> - y<sub>1</sub>) / (x<sub>2</sub> - x<sub>1</sub>). Plug in the coordinates of the two points and solve for the slope.</p><h2> What does a positive slope indicate?</h2><p>A positive slope indicates that the line is increasing from left to right. In other words, as the x-values increase, the y-values also increase.</p><h2> What does a negative slope indicate?</h2><p>A negative slope indicates that the line is decreasing from left to right. In other words, as the x-values increase, the y-values decrease.</p><h2> Can the slope of a vertical line be calculated?</h2><p>No, the slope of a vertical line is undefined. This is because the change in x-values is always 0, and division by 0 is undefined.</p>

FAQ: Learning about finding the slope of a line

What is the definition of slope?

Slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-values of two points on the line by the change in the x-values of those same points.

How do you find the slope of a line?

To find the slope of a line, you need to have two points on the line. Then, you can use the slope formula: (y2 - y1) / (x2 - x1). Plug in the coordinates of the two points and solve for the slope.

What does a positive slope indicate?

A positive slope indicates that the line is increasing from left to right. In other words, as the x-values increase, the y-values also increase.

What does a negative slope indicate?

A negative slope indicates that the line is decreasing from left to right. In other words, as the x-values increase, the y-values decrease.

Can the slope of a vertical line be calculated?

No, the slope of a vertical line is undefined. This is because the change in x-values is always 0, and division by 0 is undefined.

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