Answer
point-slope form: $y-5=6(x+2)$
slope-intercept form: $ y=6x+17$
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 $6$ and passes through the point $(-2, 5)$.
Substitute these values into the point-slope form above to obtain:
$y-5=6[x-(-2)]
\\y-5 = 6(x+2)$
(b) slope-intercept form
Substitute the slope 6 to $m$ to obtain the tentative equation:
$y=6x+b$
The line passes through $(-2, 5)$.
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:
$y=6x+b
\\5 = 6(-2) + b
\\5 = -12 + b
\\5+12 = b
\\17= b$
Thus, the equation of the line is $y=6x+17$.
