Difference of 2 perfect squares
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What is the solution in point-slope form of the line that passes through the point (3,-2) and has slope of 2/3
1 answer:
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When a line passes through the two points , its slope is given by the formula
In this question, a line L passes through the points
So, its slope is given by
When two lines are perpendicular, then the product of their slopes is -1.
Since, the slope of the line L is , so the slope of the line which is perpendicular to the given line L is
as the product of
.
check the picture below.
<h3>Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.