Answer:
[tex]y = -\frac{2}{3}x - 5[/tex]
or
2x + 3y + 15 = 0
or
2x + 3y = -15
Step-by-step explanation:
We are given an equation in standard form. To find the slope, we can convert it to slope-intercept form, which is y = mx + b.
"m" will be the slope.
Isolate "y":
3x - 2y = 3
-2y = -3x + 3
[tex]y = \frac{-3}{-2}x + \frac{3}{-2}[/tex]
[tex]y = \frac{3}{2}x - \frac{3}{2}[/tex]
The slope is 3/2.
m = 3/2
To find the slope of a perpendicular line, find the negative reciprocal by flipping the fraction and changing the negative/positive.
m⊥ = -2/3 which is: [tex]-\frac{2}{3}[/tex]
Substitute the coordinates (3, -7) and the slope into slope-intercept form.
y = mx + b Start with the general formula.
[tex]-7 = -\frac{2}{3}(3) + b[/tex]
-7 = -6/3 + b Multiply -2/3 by 3
-7 = -2 + b Add 2 to both sides to isolate "b"
-5 = b
b = -5 Keep the variable on the left side
Now we know for our new equation:
m = -2/3
b = -5
Substitute the new information into slope-intercept form.
y = mx + b
[tex]y = -\frac{2}{3}x - 5[/tex] This is the equation
You might need to convert this is standard form, which is:
ax + by = c or ax + by + c = 0
Use the form where "c" will be positive, or what your teacher prefers.
[tex]y = -\frac{2}{3}x - 5[/tex]
[tex]y + \frac{2}{3}x= -\frac{2}{3}x - 5 + \frac{2}{3}x[/tex] Add [tex]\frac{2}{3}x[/tex] to both sides
[tex]y + \frac{2}{3}x= - 5[/tex]
[tex]y + \frac{2}{3}x +5= - 5 + 5[/tex] Since "c" is negative, add 5 to both sides.
[tex]y + \frac{2}{3}x + 5= 0[/tex]
To get rid of the fraction, multiply the whole equation by "3".
[tex]3y + (3)(\frac{2}{3}x) + (3)(5)= 0[/tex]
3y + 2x + 15 = 0
2x + 3y + 15 = 0 Rearrange to follow ax + by + c = 0
2x + 3y = -15 Or rearrange to follow ax + by = c
