A Little Help Please?

Question

Can anyone tell me how to approach this problem? You don't neccesarily have to provide an answer, but thanks if you do.

Write the equation of the line that is perpenicular to the line
2x-3y=5, and passing through the y-intercept 3.

Thanks, everyone! :)

Answer 1

use the equation of a line which is y=mx+b
m=slope
b=y intercept

first find the slope of 2x-3y=5 by changing it to y=mx+b
the slope of a perpendicular line is the negative reciprocal of that line.

once you find the slope you already know the y intercept so just plug in

Answer 2

Write the equation of a line that is perpendicular to
2x - 3y = 5; passing through the y-intercept 3.

*We know the y-intercept can also be written as (0, 3).

First: place the equation in the slope-intercept form which is,
y = mx + b > subtract 2x from both sides (when you move a term to the opposite side, always use the opposite sign).

2x - 2x - 3y = -2x + 5
-3y = -2x+5

Sec: divide each term by -3.

-3y/-3 = -2x/-3 + 5/-3
y = 2x/3 - 5/3 Or, y = (2/3)x - 5/3

Now, the slope is the fraction in front of the x-variable which is, 2/3. A perpendicular line has the opposite slope - flip the fraction & change the sign (-3/2).

Third: place the perpendicular slope (-3/2) & y-intercept (0,3)in the point-slope formula which is...

y - first y= m(x - first x)
y - 3 = (-3/2)(x - 0)
y - 3 = (-3/2)(x)

*Add 3 with both sides.

y - 3 +3 = (-3/2)(x) + 3
y = (-3/2)x + 3

Answer 3

2x - 3y = 5

2x - 3y - 2x = - 2x + 5

- 3y = - 2x + 5

- 3y / - 3 = - 2x / - 3 + 5 / - 3

y = 2x / 3 - 5/3

y = 2/3x - 5/3

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Slope

m = 2/3

y intercept - 5/3

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