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 slope and values from the points in the problem gives:
#(y - color(red)(3)) = color(blue)(4/3)(x - color(red)(3))#
We can solve for #y# to transform the equation to the 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.
#y - color(red)(3) = (color(blue)(4/3) * x) - (color(blue)(4/3) * color(red)(3))#
#y - color(red)(3) = 4/3x - 4#
#y - color(red)(3) + 3 = 4/3x - 4 + 3#
#y - 0 = 4/3x - 1#
#y = color(red)(4/3)x - color(blue)(1)#
