Answer:The equation of the perpendicular line y=-1/2x+1
Explanation:
Given: The line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.
The equation of line given in standard form.
We need to write in slope-intercept form.
The general form of slope-intercept form is y = mx + b, where "m" is the slope and b is the y-intercept.
2x - y - 7 = 0
Step 1:
Add 7 on both sides, we get
2x - y - 7 + 7 = 0 + 7 [Addition of equality]
2x - y = 7
Step 2:
Subtract 2x from both sides, we get
2x - 2x - y = -2x + 7
-y = -2x + 7
Step 3:
We have negative y, we need to make it positive, so we need to multiply both sides by -1.
-1(-y) = -1(-2x + 7)
y = 2x - 7
Here slope (m) = 2 and y-intercept (b) = -7
Now we have to find the perpendicular line.
The slope of the perpendicular line is negative reciprocal of the slope of the given line.
So, m = -1/2
Now we have to find y-intercept.
We are given a point (4, -1)
Now plug in x = 4 and y = -1 in y = -1/2x + b
-1 = -1/2(4) + b
-1 = -2 + b
b = -1 +2
b = 1
So, the equation of the perpendicular line is y=-1/2x+1