Question

find the value of y so that the line passing through the two points has the given slope: 1. (6,y), (3/2, 9/5), m=2/3
2. (12,y), (-6,9/7), m=-1/6

Answer 1

Let's take the first one. We know that any line can be expressed as

y = mx + c

First we plug in the m given:

y = (2/3)x + c.

Now, we know that the point (3/2, 9/5) is on this line, so we can substitute these values into our equation to find c:

9/5 = (2/3)(3/2) + c
9/5 = 1 + c
c = 4/5

So our line is

y = (2/3)x + 4/5

Knowing that, you should be able to find the y value of the point at x = 6, to find the point (6, y).

And the second one is just like it.