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

please explain how to do at least one of them. thanks!

Answer 1

Alright so let's do the first one.

Slope, sometimes referred to as m, is the change in y between to points divided by the change in x. So the slope for the points (1,2) and (2,3) is: (3-2) / (2-1)=1/1=1

So to your problem. If we look at the points given to us we can arrange them in the same format as I did before: m=((9/5)-y) / ((3/2)-6)

Next we plug in our m value, so (2/3)=((9/5)-y) / ((3/2)-6)
Now cross multiply, meaning multiply the bottom of the fraction on one side of the equation by the top side of the fraction on the other side of the equal sign and vice versa. Cross multiplying gives us: 2*((3/2)-6)=3*((9/5)-y)

Now simplify this expression by distributing: -9=(27/5)-3y
Now solve for y: -14.4=-3y

y=24/5 (4.8)