
slopes
Each pair of points is on a line. What is the slop of each line?
A(7,5), B(2,4)
A(5,2), B(2,1)
A(3,3) B(5,3)
Write the equation for the line passing through each pair of points
(3,8), (2,6)
(2,4), (5,1)
Can someone show me how to do all of these step by step?

To calculate the slope, we use the formula (y2y1)/(x2x1)
For the first set:
A = (7,5) = (x1,y1), B = (2,4) = (x2,y2)
=> slope = (4  5)/(2  7) = 1/5 = 1/5
For the second set:
A = (5,2) = (x1,y1), B = (2,1) = (x2,y2)
=> slope = (1  2)/(2  5) = 3/3 = 1
For the third set:
A = (3,3) = (x1,y1), B = (5,3) = (x2,y2)
Here we notice the y value is the same in both coordinates, it means therefore that a horizontal line connects these two points, so the slope is 0. Nevertheless, let's go through the routine.
=> slope = (3  3)/(5 + 3) = 0/8 = 0........as expected
Now for the equation of a line section.
Recall that the equation of a line is in the form y = mx + b, where m is the slope and b is the yintercept. So first we need to find the slope of the line connecting the pair of points, then we can plug it into the above formula to find b and rewrite the formula in the form above, OR we can plug the values we know into the formula y  y1 = m(x  x1), where x1 and y1 come from any one of the points given, then you just solve for y, and your equation will be in the above formI usually use the latter approach, and that's the one I will be using. Here goes.
For (3,8) , (2,6)
slope = m = (6  8)/(2  3) = 2/1 = 2
Using (x1,y1) = (3,8)
y  y1 = m(x  x1)
=> y  8 = 2(x  3)
=> y = 2x 6 + 8
so y = 2x + 2
For (2,4) , (5,1)
slope = m = (1 + 4)/(5 + 2) = 3/5
Using (x1,y1) = (5,1)
y  y1 = m(x  x1)
=> y + 1 = (3/5)(x  5)
=> y = (3/5)x 3  1
so y = (3/5)x  4