First, we can write the equation in point-slope form. 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 values from the problem gives:
#(y - color(red)(2)) = color(blue)(7)(x - color(red)(1))#
Now, we need to convert to 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
We convert as follows:
#y - color(red)(2) = (color(blue)(7) xx x) - (color(blue)(7) xxcolor(red)(1))#
#y - color(red)(2) = 7x - 7#
#-color(blue)(7x) + y - color(red)(2) + 2 = -color(blue)(7x) + 7x - 7 + 2#
#-7x + y - 0 = 0 - 5#
#-7x + y = -5#
#-1(-7x + y) = -1 xx -5#
#(-1 xx -7x) + (-1 xx y) = 5#
#color(red)(7)x - color(blue)(1)y = color(green)(5)#
