find the value of y so that the line passing through the two points has the given slope.
1. (6,y), (3,3). m=2/3
2. (8,y), (2,-3). m=1/2
I know the formula: y2-y1/m2-m1
and I've been trying to do this for a long time now, but I still don't get it.
please help. thanks!
your formula makes no sense.
should be (y2 - y1) = m(x2 - x1)
so for the first question :
y - 3 = (2/3)(x - 3) , using the point (3,3)
3y - 9 = 2x - 6
2x - 3y = -3
now sub in the first point (6,y) to find y
12 - 3y = -3
-3y = -15
y = 5
Do the second question the same way.
Let me know what you get.
I'm still kind of confused =S
No worries! Let's break it down step by step.
1. For the first question, we have the points (6, y) and (3, 3) and the slope m = 2/3.
Apply the slope formula: (y2 - y1) / (x2 - x1) = m
Substituting the values, we get (y - 3) / (6 - 3) = 2/3.
Simplify the equation: (y - 3) / 3 = 2/3.
Cross-multiply to get: 3(y - 3) = 6.
Distribute 3 on the left side: 3y - 9 = 6.
Move -9 to the other side: 3y = 6 + 9.
Combine like terms: 3y = 15.
Divide both sides by 3: y = 15/3.
Finally, simplify: y = 5.
Therefore, the value of y is 5.
2. For the second question, we have the points (8, y) and (2, -3) and the slope m = 1/2.
Apply the slope formula: (y2 - y1) / (x2 - x1) = m
Substituting the values, we get (y - (-3)) / (8 - 2) = 1/2.
Simplify the equation: (y + 3) / 6 = 1/2.
Cross-multiply to get: 2(y + 3) = 6.
Distribute 2 on the left side: 2y + 6 = 6.
Move 6 to the other side: 2y = 6 - 6.
Combine like terms: 2y = 0.
Divide both sides by 2: y = 0/2.
Finally, simplify: y = 0.
Therefore, the value of y is 0.
I hope this explanation helps you understand how to solve these types of questions!