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
y = (2/3)x - (35/3)
Ok, I hope that helps!
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