Please help me solve this problem- Find an equation for the line perpendicular to 6x+2y=-2 having the same y-intercept as -4x-3y=6

The first equation can be rewritten as:

y=-3x-2
so the slope of the first line
is m=-3
The slope of a line perpendicular to it is
m'=1/(-3)=-1/3

The second equation can be rewritten as:
-4x-3y=6
y=(-4/3)x -2
so the y-intercept is -2.

From the above steps, there should be enough information to find the new line required using the slope-intercept form of equations.

To find the equation of a line perpendicular to a given line, we need to consider the fact that the slopes of perpendicular lines are negative reciprocals of each other.

Step 1: Find the slope of the given line.
Rewrite the given line equation in the form y = mx + b, where m is the slope and b is the y-intercept.
For the first line, 6x + 2y = -2, we can rearrange the equation to get it in slope-intercept form: y = -3x - 1/2.
So, the slope of this line is -3.

Step 2: Find the slope of the line perpendicular to the given line.
Recall that the slopes of perpendicular lines are negative reciprocals of each other. In this case, we take the negative reciprocal of -3, which is 1/3.

Step 3: Find the y-intercept of the line perpendicular to the given line.
The line perpendicular to the given line is said to have the same y-intercept as the second line, -4x - 3y = 6.

Rewrite the equation -4x - 3y = 6 in slope-intercept form: y = -4/3x - 2.
So, the y-intercept of this line is -2.

Step 4: Combine the slope and y-intercept to get the equation of the line.
We have the slope, 1/3, and the y-intercept, -2. Using the slope-intercept form (y = mx + b), we can write the equation of the line as y = 1/3x - 2.