Idk how to do this! :(

Write an equation of the line that passes through the given point and is perpendicular to the given line (1,-1), y=3x+2

For a line to be perpendicular to another line you need to use m in the linear equation of y=mx+b and find the opposite and reciprocal of that number. In this case m is 3 so the opposite of 3 is -3 and the reciprocal is just flipping the fraction of -3/1 so it is now 1/-3. Now to find it going through a certain point you just take that 1/-3 and subtract it from -1 and you will get -2/3. So the answer is y=1/-3-2/3

To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line, and then find the negative reciprocal of that slope. Let's break down the steps:

Step 1: Determine the slope of the given line.
Given line: y = 3x + 2

The given line is in slope-intercept form (y = mx + b), where 'm' represents the slope. Therefore, we can easily identify that the slope of the given line is 3.

Step 2: Find the negative reciprocal of the slope.
To find the negative reciprocal, we flip the fraction and change its sign. The negative reciprocal of 3 is -1/3.

Step 3: Use the negative reciprocal slope and the given point to find the equation.
Given point: (1, -1)

The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and 'm' is the slope. Substituting the point (1, -1) and the negative reciprocal slope (-1/3) into the equation, we get:

y - (-1) = (-1/3)(x - 1)

Simplifying and rearranging the equation, we have:

y + 1 = (-1/3)(x - 1)

To convert it to slope-intercept form, we can distribute the (-1/3) to (x - 1):

y + 1 = (-1/3)x + 1/3

Now, isolate 'y' by subtracting 1 from both sides:

y = (-1/3)x + 1/3 - 1

Simplifying further, we have:

y = (-1/3)x - 2/3

Therefore, the equation of the line that passes through the point (1, -1) and is perpendicular to the given line y = 3x + 2 is y = (-1/3)x - 2/3.