The slope of a line segment AB is 2. The coordinates of the endpoints of the line segment are A(-2,11) and (X,7). Determine the value for X.
The equation for slope is m = (y1 - y2) / (x1 - x2).
You have the slope m = 2, the point (x1, y1) = (-2, 11), and the point (x2, y2) = (X, 7).
2 = (11 - 7) / (-2 - X)
X = ?
SOMTHIN
To determine the value of X, we need to use the slope-intercept form of a line, which is given by:
y = mx + b
where m is the slope of the line.
In this case, the slope of line segment AB is given as 2. So we have:
7 = 2X + b
Now we need to find the value of b. To do this, we can use the coordinates of point A(-2,11) and substitute them into the equation above:
11 = 2(-2) + b
Simplifying this equation gives us:
11 = -4 + b
To isolate b, we add 4 to both sides:
11 + 4 = b
15 = b
Now that we have the value of b, we can substitute it back into the equation for the line to find the value of X:
7 = 2X + 15
To isolate X, we subtract 15 from both sides:
7 - 15 = 2X
-8 = 2X
Dividing both sides of the equation by 2 gives us:
X = -4
Therefore, the value of X is -4.
To find the value of X, we need to use the slope formula and the coordinates of points A and B.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
In this case, the slope (m) is given as 2. The coordinates of point A are (-2, 11), and the coordinates of point B are (X, 7).
Plugging these values into the slope formula, we get:
2 = (7 - 11) / (X - (-2))
Simplifying further:
2 = -4 / (X + 2)
To get rid of the fraction, we can cross multiply:
2(X + 2) = -4
Expanding the brackets:
2X + 4 = -4
Moving the constant term to the other side:
2X = -4 - 4
2X = -8
Dividing both sides by 2, we find:
X = -8 / 2
X = -4
Therefore, the value of X is -4.