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I didn’t understand this question please help

I didn’t understand this question please help-example-1
User Bejasc
by
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1 Answer

6 votes

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

User Matthew Rodatus
by
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