Answer:
(a) y = 4x - 15
(b) y = (-1/4)x + 2
Explanation:
The slope-intercept equation form for a line is
y = mx + b
Here m is the slope (rise/run) and b is the y-intercept ie the y-value at which the line crosses the y axis at x = 0. Drawing a picture helps
If two lines have the same slope, they are parallel
If another line has slope -(1/m) then it is perpendicular to the line with slope m
First convert the line equation into slope-intercept form as follows
8x - 2y = 1
Subtract 8x from both sides ==> -2y = 1- 8x
Multiply both sides by -1 ==> 2y = 8x - 1
Divide both sides by 2:
y = 4x - 1/2
Parallel line
y = 4x - 1/2
A parallel line should also have slope = 4
So it's equation will be of the form
y = 4x + b
To determine b, the y intercept, plug in values for x = 4, y =1 ad solve for b
1 = 4(4) + b ==> 1 = 16 + b ==> b = -15
So the equation of a line parallel to 8x - 2y = 1 passing through (4,1) is
y = 4x - 15 (Answer a)
Perpendicular Line
A perpendicular line to y = 4x - 1/2 should have the negative of the reciprocal of the slope
So the slope of the perpendicular line is -(1/4)
Equation is
y = -(1/4)x + b
Plug in the point values for (4, 1) to get
1 = - (1/4)(4) + b
1 = -1 + b
b = 2
So the equation of a line perpendicular to 8x - 2y = 1 passing through (4,1) is y = -(1/4)x + 2