Final answer:
To find the value of x, we can substitute the coordinates (-4,-14) in the equation of the perpendicular line.
Step-by-step explanation:
The line passing through the points (-1,-2) and (3,-4) can be found by finding the slope of the line that connects these points. The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-1,-2) and (3,-4) in the formula, we have:
m = (-4 - (-2)) / (3 - (-1)) = (-4 + 2) / (3 + 1) = -2 / 4 = -1/2
A line perpendicular to another line has a slope that is the negative reciprocal of the slope of the original line. The negative reciprocal of -1/2 is 2.
So, the perpendicular line has a slope of 2. Using the point (-4,-14) and the slope of 2 in the point-slope form of a line equation, we have:
y - y1 = m(x - x1)
y - (-14) = 2(x - (-4))
y + 14 = 2(x + 4)
y + 14 = 2x + 8
y = 2x - 6
This is the equation of the line perpendicular to the line passing through (-1,-2) and (3,-4). To find the value of x, we can substitute the coordinates (-4,-14) into the equation:
-14 = 2x - 6
-14 + 6 = 2x
-8 = 2x
x = -4
Therefore, the value of x is -4.