Question

OK this is another question which I need help on please please help if you can. CAUSED ME MUCH DISTRESS

Answer 1

15 = 2x - 3y

Explanation:

We have the two points P1(3,-3) and P2(9,1).

First, calculate the slope between those points:

slope
`= (y_2 - y_1)/(x_2 - x_1) = (1 - (-3))/(9 - 3) = (4)/(6) = (2)/(3)`

Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):

(3,-3)

---> (2, -3 - (2/3)) = (2,-3 2/3)

---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)

---> (0, (-4 1/3) - 2/3) = (0,-5)

This tells us, that our line intersects the y-axis at (0,-5).

The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.

In our case: f(x) = y = (2/3)x -5.

To get it into the correct form, we simply subtract y from both sides and get:

0 = (2/3)x - y - 5

To get only integers just multiply everything with 3 and add 15 and get:

15 = 2x - 3y, which fulfils the form asked for in the problem.