We can use the point-slope formula to find an equation for this line. 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 information from the problem gives:
#(y - color(red)(4)) = color(blue)(-5)(x - color(red)(3))#
Or we can convert to the slope-intercept form by solving for #y#. 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)(4) = (color(blue)(-5) xx x) - (color(blue)(-5) xx color(red)(3))#
#y - color(red)(4) = -5x + 15#
#y - color(red)(4) + 4 = -5x + 15 + 4#
#y - 0 = -5x + 19#
#y = color(red)(-5)x + color(blue)(19)#
Or, we can transform this equation into standard form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
#5x + y = 5x + color(red)(-5)x + color(blue)(19)#
#5x + y = 0 + 19#
#color(red)(5)x + color(blue)(1)y = color(green)(19)#
