Calculate the slope of the line through the points (6,-8) and (3,-4)
1 answer:
Answer:
a. y=-4/3 x
b. Yes because the point makes the equation true.
Step-by-step explanation:
To write the equation of a line we must have a slope and a point. To find the slope we use the slope formula and substitute (x,y) points in it as shown below:
Now that we have the slope, plug in the slope and choose one point to plug into the point slope formula. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y--4)=-4/3(x-3)
y+4=-4/3(x-3)
y+4=-4/3x +4
y=-4/3x
Test (-3,4): 4= -4/3 (-3)
4=4 Yes
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Answers:
a = -6/37
b = -1/37
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Explanation:
Let's start things off by computing the derivatives we'll need
Apply substitution to get
I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.
The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero
a-6b = 0
a = 6b
At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)
-6a -b = 1
-6(6b) - b = 1 .... plug in a = 6b
-36b - b = 1
-37b = 1
b = -1/37
Use this to find 'a'
a = 6b
a = 6(-1/37)
a = -6/37