Answer:
The equation of line in point slope form is: [tex]\mathbf{y+5=-\frac{2}{3} (x-4)}[/tex]
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: [tex]y-y_1=m(x-x_1)[/tex]
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 [tex]y=mx+b[/tex] 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 [tex]x_1=4, y_1=-5[/tex] and slope is: m=-2/3
So, equation of line in point-slope form is:
[tex]y-y_1=m(x-x_1)\\y-(-5)=-\frac{2}{3}(x-4)\\y+5=-\frac{2}{3}(x-4)[/tex]
So, the equation of line in point slope form is: [tex]\mathbf{y+5=-\frac{2}{3} (x-4)}[/tex]
Option A is correct option.
