Answer:
y=3x+1 or 3x-y=-1
Step-by-step explanation:
Hello,
We are given the line 3y+x=-2, and we want to write an equation of the line that is perpendicular to 3y+x=-2, and contains the point (-2, -5)
First, we'll need to find the slope of 3y+x=-2, as perpendicular lines have slopes that multiply to -1
In order to find the slope of 3y+x=-2, let's convert the equation of the line from standard form to slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
y is isolated by itself in slope-intercept form, so let's subtract x from both sides of the equation
3y=-x-2
Now divide both sides by 3
y=[tex]-\frac{1}{3}x - \frac{2}{3}[/tex]
The slope of the line is -1/3
Now to find the slope of the line perpendicular to it, use this formula:
-1/3m=-1
Multiply both sides by -3
m=3
So the slope of the line perpendicular to it is 3
We can write the equation of this new line in slope-intercept form; substitute 3 as m in y=mx+b:
y=3x+b
Now we need to find b
As the equation passes through the point (-2, -5), we can use its values to help solve for b
Substitute -2 as x and -5 as y:
-5=3(-2)+b
Multiply
-5=-6+b
Add 6 to both sides
1=b
Substitute 1 as b:
y=3x+1
The equation can be left as this, or we can write it in standard form, if you wish
In standard form, x and y are on the same side; so we'll subtract 3x from both sides in order to have both variables on the same side
-3x+y=1
However, a (the coefficient in front of x) cannot be negative; so we'll multiply both sides by -1 to change the sign of the variable.
3x-y=-1
Hope this helps!
