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To find the slope, you must have at least two points, not one. You cannot find the slope at one point, because coordinate points do not have slopes - lines have slopes.
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
If it is the equation for a line, then it can be rearranged into the format y = mx + b, where m is the slope of the line, and b is the point where the line intercepts the y-axis.If it is not for a straight line, then the slope is changing with x, and the derivative of the function would find the slope at a particular x.
According to the question, you HAVE the point!
y-4=3/2(x-7)
You use point-slope form to find the equation of a line if you only have a point and a slope or if you are just given two point. Usually you will convert point-slope form to slope-intercept form to make it easier to use.
By differentiating the answer and plugging in the x value along the curve, you are finding the exact slope of the curve at that point. In effect, this would be the slope of the tangent line, as a tangent line only intersects another at one point. To find the equation of a tangent line to a curve, use the point slope form (y-y1)=m(x-x1), m being the slope. Use the differential to find the slope and use the point on the curve to plug in for (x1, y1).
You find the slope of the tangent to the curve at the point of interest.
You find the tangent to the curve at the point of interest and then find the slope of the tangent.
To find the slope, you must have at least two points, not one. You cannot find the slope at one point, because coordinate points do not have slopes - lines have slopes.
Use point-slope formula
If you want to find the initial value of an exponential, which point would you find on the graph?
If it is the equation for a line, then it can be rearranged into the format y = mx + b, where m is the slope of the line, and b is the point where the line intercepts the y-axis.If it is not for a straight line, then the slope is changing with x, and the derivative of the function would find the slope at a particular x.
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
According to the question, you HAVE the point!
To find the maximum speed in a time-position graph, you would need to locate the steepest slope or the point with the highest gradient on the graph. This slope represents the highest rate of change in position over time, which corresponds to the maximum speed.
y-4=3/2(x-7)