Identify an equation in point-slope form the line parallel to y=-2/3x+8 that passes through(4, -5). A. y+5=-2/3(x-4)
B. y-5=-2/3(x+4)
C. y+5=3/2(x-4)
D. y-4=2/3(x+5)

The equation of line in point slope form is:

Option A is correct option.

Step-by-step explanation:

We need to identify an equation in point-slope form the line parallel to y=-2/3x+8 that passes through(4, -5).

The general equation of point slope form is:

where m is slope of the equation.

Finding slope of the equation.

Since the two lines are parallel so, both lines have same slope.

Equation of given line: y=-2/3x + 8

This equation is in slope-intercept form, comparing with general equation where m is slope , we get the value of m= -2/3

So, slope of given line = m = -2/3

Slope of required line = m =-2/3

Now, writing equation in point-slope form:

We are given point (4,-5) so, we have and slope is: m=-2/3

So, equation of line in point-slope form is:

So, the equation of line in point slope form is:

Option A is correct option.