To determine the equation of the line through the points (2, -4) and (x, 1) with a slope of -5, you can use the point-slope form of the equation of a line:

y - y_1 = m(x - x_1)

where (x1, y1) is a point on the line, m is the slope, and (x, y) are the coordinates of any other point on the line.

In this case, you have the point (2, -4) and the slope m = -5:

y - (-4) = -5(x - 2)

Now, simplify the equation:

y + 4 = -5(x - 2)

Next, distribute the -5 on the right side:

y + 4 = -5x + 10

Now, isolate y by subtracting 4 from both sides:

y = -5x + 6

So, the equation of the line is y = -5x + 6.

To find the value of x, you can use the fact that the line passes through the point (x, 1). Substitute this point into the equation:

1 = -5x + 6

Now, solve for x:

5x = 6 - 1

5x = 5

x = 1

So, the value of x is 1.