How do you write an equation in point slope form parallel to -2x-3y = -2 and passing through (2, -2)?

Question

Avery Alexander · Accepted Answer

Since the lines are parallel, this means that their slope is equal.

#-2x - 3y = -2# #-3y = -2 + 2x# #y = 2/3 - 2/3x# The slope is #-2/3# We can now use the point and the slope to the find the equation of the line by plugging our values into point slope form. #y - y_1 = m(x - x_1)# #y - (-2) = -2/3(x - 2)# #y + 2 = -2/3x + 4/3# #y = -2/3x - 2/3# Hopefully this helps!

Savannah Anderson · Answer

undefined To write an equation in point-slope form parallel to the given line -2x - 3y = -2 and passing through the point (2, -2), you need to determine the slope of the given line and then use that slope to construct the equation.

First, rearrange the given equation into slope-intercept form (y = mx + b):
-2x - 3y = -2
-3y = 2x - 2
y = (2/3)x - 2/3

The slope of the given line is 2/3.

Since the line we're looking for is parallel to this line, it will have the same slope.

Now, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)

Using the given point (2, -2) and the slope (2/3):
y - (-2) = (2/3)(x - 2)

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

This is the equation in point-slope form parallel to the given line and passing through the point (2, -2).