Points R=(6,4), Q=(4,3), and P=(-2,b) are collinear. What is the value of b?

the line through R and Q is

(y-4)/(x-6) = (3-4)/(4-6)
or
y = x/2 + 1

so, for (-2,b) to be on the same line,

b = -2/2 + 1 = 0

Solve this question

Well, if points R and Q are collinear with point P, that means they all lie on the same line. So, we can use the slope formula to find the value of b.

The slope between points R and Q is (4-3)/(6-4) = 1/2.

Since points P and Q are also collinear, they must have the same slope.

So, (b-3)/(-2-4) = 1/2.

Cross multiplying, we get 2(b-3) = -2(-6).

Simplifying, we have 2b - 6 = 12.

Adding 6 to both sides, we get 2b = 18.

Finally, dividing both sides by 2, we find that b = 9.

Therefore, the value of b is 9.

To determine the value of b, we need to confirm that the points R, Q, and P are collinear.

Collinear points lie on the same line. To check if three points are collinear, we can use the concept of slope.

The slope (m) between two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Let's calculate the slope between points R and Q:
m(RQ) = (3 - 4) / (4 - 6) = -1 / -2 = 1/2

Now, we'll calculate the slope between points Q and P:
m(QP) = (b - 3) / (-2 - 4) = (b - 3) / -6

Since R, Q, and P are collinear, the slopes between R and Q and between Q and P should be equal:
m(RQ) = m(QP)

So, we can set up an equation:
1/2 = (b - 3) / -6

To solve for b, we can cross-multiply:
1 * -6 = 2 * (b - 3)
-6 = 2b - 6

Next, we'll isolate b by adding 6 to both sides:
-6 + 6 = 2b - 6 + 6
0 = 2b

Finally, we solve for b by dividing both sides of the equation by 2:
0 / 2 = 2b / 2
0 = b

Therefore, the value of b is 0. The collinear points R=(6,4), Q=(4,3), and P=(-2,0).

To determine the value of b, we need to find the equation of the line passing through points R and Q. Once we have the equation of the line, we can substitute the x-coordinate of point P, which is -2, and solve for the y-coordinate, which will give us the value of b.

First, let's calculate the slope (m) of the line passing through points R and Q using the formula:

m = (y2 - y1) / (x2 - x1)

m = (3 - 4) / (4 - 6)
m = -1 / -2
m = 1/2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line passing through points R and Q:

y - y1 = m(x - x1)

Using point R (6, 4) as a reference:

y - 4 = (1/2)(x - 6)

Now we can substitute the x-coordinate of point P, which is -2, into the equation:

b - 4 = (1/2)(-2 - 6)

Simplifying the equation:

b - 4 = (1/2)(-8)
b - 4 = -4
b = -4 + 4
b = 0

Therefore, the value of b in order for points R, Q, and P to be collinear is 0.