Answer
point-slope form: $y+1=8(x-4)$
slope-intercept form: $y=8x-33$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where m = slope and b = y-intercept
(2) The point-slope form of a line's equation is:
$y-y_1=m(x-x_1)$
(a) point-slope form
The given line has a slope of $8$ and passes through the point $(4, -1)$.
Substitute these values into the point-slope form above to obtain:
$y-(-1)=8(x-4)
\\y+1 = 8(x-4)$
(b) slope-intercept form
Substitute the slope 8 to $m$ to obtain the tentative equation:
$y=8x+b$
The line passes through $(4, -1)$.
This means that the coordinates of this point satisfy the equation of the line. Substitute the x and y-coordinates of this point into the tentative equation to obtain:
$y=8x+b
\\-1 = 8(4) + b
\\-1 = 32 + b
\\-1-32 = b
\\-33= b$
Thus, the equation of the line is $y=8x-33$.
