Right the slope intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

Question

1) Point: (2,1)

Line: 4x-2y=3

2) Point: (-2/3,7/8)

Line: 3x+4y=7

3) Point: (3,-2)

Line: x-4=0

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the equations both perpendicular and parallel to the given equations.

1) Given 4x - 2y = 3 passing through point (2,1). We put the equation in slope-intercept form to get the slope such that y = 2x - (3/2) after solving for y. The parallel line uses the slope from the given equation such that y - y1 = 2(x- x1). Then we plug in the point (2,1) and solve for y to get the parallel line!

For the perpendicular line, we take the reciprocal of the slope 2 to get (-1/2) and pull out the point-slope formula such that y - y1 = (-1/2)(x - x1)......We plug in point (2,1) for (x1, y1), then solve for y to get the line perpendicular to y = 2x - (3/2)!

Repeat this process for the next two problems listed!

I hope this helped!

Answer 2

Hi Ayanna R.,

Parallel to the given line: just keep the equation the same except for the constant, plug in the given point to find that. Then reset to slope - intercept form.

Perpendicular to the given line: rewrite the parallel line equations you just found, but with m(perp) = -(1/m(para)). Then re-plug in the given point to find the new intercept as well.

So example, 4x - 3y = Q ; 4(2)-3(1) = Q = 5 so 4x - 3y = 5 is parallel, or: parallel: y = (4/3)x - (5/3)

For perp: y = (-1/(4/3))x + P ; 1 = (-3/4)2 + P ; P = 2.5 ; perpendicular: y = (-3/4)x + 2.5

Unless I made a silly calculation error, that is --

-- Cheers, -- Mr. d.

Answer 3

For equation in standard form: ax + by = c, slope = -a/b

1) Slope of 4x - 2y = 3, slope = -4/-2 = 2

Slope of parallel line is 2

slope-intercept form

y = mx + b

Plug in (2,1) for (x,y) and 2 for m to determine b

1 = 2(2) + b

b= -3

equation is y = 2x -3

Slope of perpendicular line is -1/2

Plug in (2,1) for (x,y) and -1/2 for m to determine b

1 = -1/2(2) + b

b = 2

equation is y = -1/2x + 2

2) is done similarly to 1)

3) Line is x=4, which has undefined slope.

Line parallel to it going through (3,-2), would be x=3

Line perpendicular to it going through (3,-2) would be y= -2