To find the slope we must put the equation in slope-intercept form.
The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
Solving for #y# gives:
#7x = 4y + 12#
#7x - color(red)(7x) - color(blue)(4y) = 4y + 12 - color(red)(7x) - color(blue)(4y)#
#7x - color(red)(7x) - color(blue)(4y) = 4y - color(blue)(4y) - color(red)(7x) + 12#
#0 - 4y = 0 - 7x + 12#
#-4y = -7x + 12#
#(-4y)/color(red)(-4) = (-7x + 12)/color(red)(-4)#
#(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = (-7x)/color(red)(-4) + 12/color(red)(-4)#
#y = color(red)(7/4)x - color(blue)(3)#
Therefore the slope is #color(red)(m =7/4)#
