write an equation in slope-intercept form for the line described.
perpendicular to y=one over two times a number minus one,x-intercept at 4
To find the equation of a line perpendicular to the given line with an x-intercept at 4, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line is y = (1/2)x - 1, which is in slope-intercept form (y = mx + b) with a slope of 1/2. The perpendicular line will have a slope that is the negative reciprocal of 1/2, which is -2.
Now, to find the equation with a given x-intercept at 4, we know that when x = 4, y = 0 (x-intercept condition). Using the slope-intercept form, we can substitute the values into the equation:
y = mx + b
0 = -2(4) + b
0 = -8 + b
b = 8
Therefore, the equation of the line perpendicular to y = (1/2)x - 1 with an x-intercept at 4 is y = -2x + 8 in slope-intercept form.