SOLUTION: Find the value of a if the interval joining (-5, -2) and (-3, a) has a gradient of -3/4. Thanks.

Question 1009166: Find the value of a if the interval joining (-5, -2) and (-3, a) has a gradient of -3/4.
Thanks.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Using the template y = Mx + b
Use the point (-5,-2). Substitute -5 for x, -2 for y and
-3/4 for M
-2 = (-3/4)(-5) + b
-2 = 15/4 + b
add -15/4 to each side
-2 -15/4 = b
-8/4 -15/4 = b
-23/4 = b
So our equation is y = (-3/4) x -23/4
To solve for a in the pair (-3,a) , substitute a for y, and -3 for x
a = (-3/4)(-3) -23/4
a = 9/4 -23/4
a = -14/4
a = -7/2
our two points are (-5,-2) and (-3,-7/2)
We can verify our result.
The gradient = (y2-y1)/(x2-x1)
(-7/2-(-2))/(-3-(-5)) =
(-7/2 + 4/2)/(-3+5)
(-3/2)/2
-3/4

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