Question

find the slope of the line given by each equation
(1) 7x+13y=91


(2) 7-3y=9x

Answer 1

to find the slope of the line, we transform this given equation in the form,
y = mx + b
where m = slope and b = y-intercept
thus for (1) 7x + 13y = 91, we first divide all term by numerical coefficient of y (which is 13) to get y alone:
(7/13)x + (13/13)y = 91/13
(7/13)x + y = 7
now, to have this in the form y = mx + b, we transpose (7/13)x to the other side of equation,, to do this we change its sign from positive to negative:
y = 7 - (7/13)x or
y = -(7/13)x + 7
thus m = slope = -(7/13)

for (b), we do the same thing:
7 - 3y = 9x
we transpose 7 to other side, changing its sign from positive to negative:
-3y = 9x - 7
then we divide all terms by -3 to get y alone:
y = 9/(-3) x - 7/(-3)
y = -3x + (7/3)
thus m = slope = -3

hope this helps~ :)