Question

What is the equation, in point-slope form, for a line that goes through (8,−4) and has a slope of −5/6 ?

Answer 1

The equation of a line in point-slope is given by ,
y-y1=m(x-x1)
where m is the slope of the line which passes through (x1, y1)
Therefore
y-(-4) = -5/6(x-8)
y+4 = -5/6(x-8)
6y+24 = -5x+40
5x+6y+24-40=0
5x+6y-16=0

Answer 2

Answer:

The point slope form of line is $y+4=-\frac{5}{6}(x-8)$.

Step-by-step explanation:

If a line passing through the point $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

It is given that the line passing through the point (8,−4) and has a slope of −5/6. So, the point slope form of line is

$y-(-4)=\frac{-5}{6}(x-8)$

$y+4=-\frac{5}{6}(x-8)$

Therefore the point slope form of line is $y+4=-\frac{5}{6}(x-8)$.