The slope of a line is -2 and the line contains the points (7,4) and (x,12). What is the value of x?
since the slope is -2, y decreases by 2 when x increases by 1.
since y increased by 8, x decreased by 4, so (3,12) is the other point.
Well, let's see if we can solve this problem step by step. The slope of the line is -2, so we have m = -2. We also know that the line passes through the points (7,4) and (x,12).
To find the value of x, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
So, let's plug in the values we know:
-2 = (12 - 4) / (x - 7)
Now, let's do some math to solve for x. We can start by multiplying both sides of the equation by (x - 7):
-2(x - 7) = 12 - 4
-2x + 14 = 8
Next, we'll subtract 14 from both sides:
-2x = 8 - 14
-2x = -6
Finally, we'll divide both sides by -2 to solve for x:
x = -6 / -2
x = 3
So, the value of x is 3. That's a wrap!
To find the value of x, we can use the formula for the slope of a line:
m = (y₂ - y₁) / (x₂ - x₁)
Given that the slope (m) is -2, and the points are (7,4) and (x,12), we can substitute the values into the formula:
-2 = (12 - 4) / (x - 7)
Now we can solve for x:
-2 = 8 / (x - 7)
Multiply both sides of the equation by (x - 7):
-2(x - 7) = 8
Expand and simplify:
-2x + 14 = 8
Subtract 14 from both sides:
-2x = 8 - 14
-2x = -6
Divide both sides of the equation by -2:
x = -6 / -2
Simplify:
x = 3
Therefore, the value of x is 3.
To find the value of x, we'll use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -2, we can substitute this value into the slope-intercept equation as follows:
y = -2x + b
Next, we need to find the value of b. We can do this by substituting the coordinates of one of the given points into the equation.
Let's use the point (7,4). We can substitute x = 7 and y = 4 into the equation:
4 = -2(7) + b
Simplifying the equation, we get:
4 = -14 + b
To isolate b, we can add 14 to both sides of the equation:
4 + 14 = b
18 = b
Now, we have the value of b, which is 18. Substituting this value back into the slope-intercept equation, we get:
y = -2x + 18
Finally, we are given another point on the line, (x,12). We can substitute this point into the equation:
12 = -2x + 18
To find the value of x, we'll isolate it on one side of the equation. First, we can subtract 18 from both sides:
12 - 18 = -2x
-6 = -2x
To solve for x, we divide both sides by -2:
-6 / -2 = x
3 = x
Therefore, the value of x is 3.