SOLUTION: Find the slope of the line through the points P and Q when: a. P(1,3) and Q(x, x2+3x-1) b. P(x, x2+3x-1) and Q(x+h, (x+h)2+3(x+h)-1)

Algebra ->  Test -> SOLUTION: Find the slope of the line through the points P and Q when: a. P(1,3) and Q(x, x2+3x-1) b. P(x, x2+3x-1) and Q(x+h, (x+h)2+3(x+h)-1)      Log On


   

Question 1133393: Find the slope of the line through the points P and Q when:
a. P(1,3) and Q(x, x2+3x-1)
b. P(x, x2+3x-1) and Q(x+h, (x+h)2+3(x+h)-1)
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a. P(1,3) and Q(x, x%5E2%2B3x-1)

slope=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29


slope=%28x%5E2%2B3x-1-3%29%2F%28x-1%29

slope=%28x%5E2%2B3x-4%29%2F%28x-1%29

slope=%28x%5E2-x%2B4x-4%29%2F%28x-1%29

slope=%28%28x%5E2-x%29%2B%284x-4%29%29%2F%28x-1%29

slope=%28x%28x-1%29%2B4%28x-1%29%29%2F%28x-1%29

slope=%28%28x%2B4%29%28x-1%29%29%2F%28x-1%29

slope=%28%28x%2B4%29cross%28%28x-1%29%29%29%2Fcross%28%28x-1%29%29

slope=x%2B4


b. P(x, x%5E2%2B3x-1) and Q(x%2Bh, (%28x%2Bh%29%5E2%2B3%28x%2Bh%29-1)

slope=%28%28x%2Bh%29%5E2%2B3%28x%2Bh%29-1-%28x%5E2%2B3x-1%29%29%2F%28x%2Bh-x%29

slope=%28h%5E2+%2B+2hx+%2B+x%5E2%2B3x%2B3h-1-x%5E2-3x%2B1%29%2Fh



slope=%28h%5E2+%2B+2hx+%2B3h%29%2Fh

slope=h%28h+%2B+2x+%2B3%29%2Fh

slope=cross%28h%29%28h+%2B+2x+%2B3%29%2Fcross%28h%29

slope=+2x%2Bh+%2B3



Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
slope = rise/run = (y2 -y1)/(x2 -X1) where (x1,y1) and (x2,y2) are two points
:
a) slope = (x^2+3x-1 -3)/(x-1) = ((x+4)*(x-1))/(x-1) = x+4
:
b) slope = ((x+h)^2+3(x+h)-1 -(x^2+3x-1))/(x+h-x) = (x^2+2xh+h^2+3x+3h-1-x^2-3x+1)/h = (h^2+3h+2xh)/h = h+2x+3
:
Note assume h is not equal to 0
: