Answer
point-slope form: $y-5=2(x-3)$
slope-intercept form: $y = 2x -1$
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 $2$ and passes through the point $(3, 5)$.
Substitute these values into the point-slope form above to obtain:
$y-5=2(x-3)$
(b) slope-intercept form
Substitute the slope 2 to $m$ to obtain the tentative equation:
$y=2x+b$
The line passes through $(3, 5)$.
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:
$y=2x=b
\\5 = 2(3) + b
\\5 = 6 + b
\\5-6 = b
\\-1 = b$
Thus, the equation of the line is $y=2x-1$.
