 Hi, and welcome to the session. Let us discuss the following question. The question says, proofs out the line through the point x1, y1, and parallel to line. Ax plus vy plus c is equal to 0. Is a into x minus x1 plus b into y minus y1 is equal to 0. Let's now begin with the solution. In this question, we will first find the slope of this line. Since the line passing through x1, y1 is parallel to this line, therefore slope of parallel line is also equal to slope of this line. And finally, by using the equation of line passing through point x1, y1, and having slope m, we will prove that equation of line through the point x1, y1, and parallel to this line is a into x minus x1 plus b into y minus y1 is equal to 0. Now the given line is ax plus vy plus c is equal to 0. This implies vy is equal to minus ax minus c. This implies y is equal to minus a by bx minus c by b. Now this equation is of the form y is equal to a mix plus c. On comparing this equation with y is equal to a mix plus c, we find that slope of this line is minus a by b. So slope of line ax plus vy plus c is equal to 0 is minus a by b. Now the line passing through x1, y1 is parallel to this line. Therefore slope of parallel line is also minus a by b. Now equation of line passing through x1, y1 and having slope minus a by b is y minus y1 is equal to minus a by b into x minus x1, right? Now this implies b into y minus y1 is equal to minus a into x minus x1. This implies a into x minus x1 plus b into y minus y1 is equal to 0. Hence we have proved that equation of line passing through the point x1, y1 and parallel to the line ax plus b plus c is equal to 0 is a into x minus x1 plus b into y minus y1 is equal to 0. This completes the session by and take care.