Find an equation for the line in the form ax + by c. where a. b. and c are integers with no factor common to all three and a 20. Through (1. -6), perpendicular to x + y = 2 The equation of the line is (Type an equation)

Answer:a = 1, b = -1 and c = 7Step-by-step explanation:Since, when two lines are parallel then the product of their slope is -1,Also, the slope intercept form of a line is y = mx + c,Where, m is the slope of the line,x + y = 2  ⇒ y = -x + 2Thus, the slope of the line x + y = 2 is -1,Let [tex]m_1[/tex] is the slope of the line that is perpendicular to x + y = 2,By the above statement,[tex]m_1\times -1=-1\implies m_1 = 1[/tex]Suppose y = x + c is the line perpendicular to the line x + y = 2,According to the question,y = x + c is passes through the point (1,-6),⇒ -6 = 1 + c ⇒ -6 - 1 = c ⇒ c = -7Hence, the equation of the required line is,y = x - 7 ⇒ x - y = 7Compare this with standard form of line ax+by=cWe get, a = 1, b = -1 and c = 7