The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the point and the slope from the problem gives:
#(y - color(red)(4)) = color(blue)(-3/4)(x - color(red)(6))#
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.
We can solve the equation above for #y# to put it into this form.
#y - color(red)(4) = (color(blue)(-3/4) xx x) - (color(blue)(-3/4) xx color(red)(6))#
#y - color(red)(4) = -3/4x + 18/4#
#y - color(red)(4) + 4 = -3/4x + 18/4 + 4#
#y - 0 = -3/4x + 18/4 + (4/4 xx 4)#
#y = -3/4x + 18/4 + 16/4#
#y = -3/4x + 34/4#
