Question

3) FInd an equation of the line containting the given pair of points.
(3,4) and (9,6)

MY ANSWEAR: 2/5X+9

4)Find an equation of the line having the given slope and containing the given point.
m=2/3 (7,-7)

MY ANSWEAR: 2/3X-14/3X

Answer 1

Okay, first we need to get the slope of the line connecting the two given points by using:

Slope (m) = (y2 - y1)/(x2 - x1)

Therefore: m = (6 - 4)/(9 - 3)
m = 2/6 = 1/3

So the slope of the line joining (3,4) and (9,6) is 1/3.

To find the equation of the line use the equation:
y - y1 = m(x - x1)

You can use either point for the (x1,y1)
I'll use (3,4)

So we get:
y - 4 = (1/3)*(x - 3)
3*(y - 4) = (x - 3)
3y - 12 = x - 3
3y = x - 3 + 12
3y = x + 9
y = (1/3)*x + 3

So y = (1/3)x + 3 is your equation for the line for part 3).

For part 4) you can go straight to the
y - y1 = m(x - x1) equation.

So subbing in we get:

y - (-7) = (2/3)*(x - 7)
y + 7 = (2/3)*(x - 7)
3*(y + 7) = 2*(x - 7)
3y + 21 = 2x - 14
3y = 2x - 14 - 21
3y = 2x - 35

So
y = (2/3)x - (35/3)

Ok, I hope that helps!