Find the value of x if the slope of the line segment joining (3/10,6) and (x,-4) is 5.
(-4 -6)/(x -0.3) = 5
-10/(x-0.3) = 5
-10 = 5x -1.5
5x = -8.5
x = -1.7
To find the value of x, we need to use the formula for calculating the slope of a line segment.
The formula for slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
We are given:
Point 1: (3/10, 6) with coordinates (x1, y1)
Point 2: (x, -4) with coordinates (x2, y2)
Slope: 5
Substituting the given values into the formula, we have:
5 = (-4 - 6) / (x - 3/10)
Now we can solve for x. Multiply both sides of the equation by (x - 3/10):
5(x - 3/10) = -10
Distribute 5 to both terms:
5x - 3/2 = -10
To eliminate the fraction, we can multiply both sides of the equation by 2:
2(5x - 3/2) = 2(-10)
10x - 3 = -20
Add 3 to both sides of the equation to isolate the variable:
10x = -20 + 3
10x = -17
Now, divide both sides of the equation by 10:
x = -17/10
Therefore, the value of x is -17/10.