Question

The slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?
y – 13 = 5(x – 2)
y + 13 = 5(x + 2)
y – 2 = 5(x – 13)
y + 2 = 5(x + 13)

Answer 1

we know that

the point-slope form of the equation of the line is

$y-y1=m(x-x1)$

in this problem we have

$m=5$ ----> given line

$(x1,y1)=(-2,-13)$

substitute in the equation of the line

$y-(-13)=5(x-(-2))$  

$y+13=5(x+2)$  

therefore

the answer is the option

$y+13=5(x+2)$  

Answer 2

Forget the best choice answer would be the second one because point slope form is y1 - y2 = slope (x1 - x2) if the x or y is negative you do the iverse to make it positive in point slope equation