Each pair of points lies on a line with the given slope. Find x
(2,4) (x,8). Slope is -2
(8-4)/(x-2) = -2
4/(x-2) = -2
4 = -2(x-2)
x-2 = -2
X = 0.
To find the value of x, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (2, 4) and (x2, y2) = (x, 8).
Given slope m = -2, we can substitute the known values:
-2 = (8 - 4) / (x - 2)
Now, let's solve for x. First, multiply both sides of the equation by (x - 2):
-2(x - 2) = 8 - 4
-2x + 4 = 4
Next, subtract 4 from both sides:
-2x = 4 - 4
-2x = 0
Finally, divide both sides by -2:
x = 0
Therefore, x = 0.
To find the value of x, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Where:
m is the slope of the line and
b is the y-intercept.
In this case, the slope (m) is already given as -2. We have two points: (2,4) and (x,8).
Let's substitute the coordinates of the first point (2,4) into the equation:
4 = -2(2) + b
Simplifying the equation:
4 = -4 + b
To isolate b, we add 4 to both sides of the equation:
4 + 4 = -4 + 4 + b
8 = b
Now that we know the y-intercept (b) is 8, we substitute it and the slope (m = -2) into the equation:
y = -2x + 8
We can substitute the y-coordinate of the second point, (x,8), which is 8:
8 = -2x + 8
To solve for x, we isolate the variable x:
8 - 8 = -2x + 8 - 8
0 = -2x
Divide both sides by -2:
0 / -2 = -2x / -2
0 = x
Therefore, x is equal to 0.
since the slope is -2, and y changed from 4 to 8 (4),
x changes by -1/2 * 4 = -2
So, x = 0