Using point-slope formula for calculating equation of the line; y - y1 = m (x – x1) Where x1 and y1 is the point (0,2), i.e. x1 = 0 and y1 = 2 and slope = m = 2/3 Putting all values; y – 2 = 2/3 (x – 0) y – 2 = 2/3x 3y – 6 = 2x --------------- (1) Now put (-3,0) in equation (1), i.e. x = -3 and y = 0; – 6 = – 6 Hence (-3,0) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Now checking other points, whether it satisfies the equation of line or not. putting (-2,-3) in equation (1); - 9 - 6 = - 4 (-2,-3) does not lie on the line. Putting (2,5) in equation (1); 15 – 6 = 4 (2,5) does not lie on the line. Putting (3,4) in equation (1); 12 – 6 = 6 6 = 6 Hence (3,4) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Putting (6,6) in equation (1); 18 – 6 = 12 12 = 12 Hence (6,6) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Using point-slope formula for calculating equation of the line; y - y1 = m (x – x1) Where x1 and y1 is the point (0,2), i.e. x1 = 0 and y1 = 2 and slope = m = 2/3 Putting all values; y – 2 = 2/3 (x – 0) y – 2 = 2/3x 3y – 6 = 2x --------------- (1) Now put (-3,0) in equation (1), i.e. x = -3 and y = 0; – 6 = – 6 Hence (-3,0) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Now checking other points, whether it satisfies the equation of line or not. putting (-2,-3) in equation (1); - 9 - 6 = - 4 (-2,-3) does not lie on the line. Putting (2,5) in equation (1); 15 – 6 = 4 (2,5) does not lie on the line. Putting (3,4) in equation (1); 12 – 6 = 6 6 = 6 Hence (3,4) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Putting (6,6) in equation (1); 18 – 6 = 12 12 = 12 Hence (6,6) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line.Using point-slope formula for calculating equation of the line; y - y1 = m (x – x1) Where x1 and y1 is the point (0,2), i.e. x1 = 0 and y1 = 2 and slope = m = 2/3 Putting all values; y – 2 = 2/3 (x – 0) y – 2 = 2/3x 3y – 6 = 2x --------------- (1) Now put (-3,0) in equation (1), i.e. x = -3 and y = 0; – 6 = – 6 Hence (-3,0) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Now checking other points, whether it satisfies the equation of line or not. putting (-2,-3) in equation (1); - 9 - 6 = - 4 (-2,-3) does not lie on the line. Putting (2,5) in equation (1); 15 – 6 = 4 (2,5) does not lie on the line. Putting (3,4) in equation (1); 12 – 6 = 6 6 = 6 Hence (3,4) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Putting (6,6) in equation (1); 18 – 6 = 12 12 = 12 Hence (6,6) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line.Using point-slope formula for calculating equation of the line; y - y1 = m (x – x1) Where x1 and y1 is the point (0,2), i.e. x1 = 0 and y1 = 2 and slope = m = 2/3 Putting all values; y – 2 = 2/3 (x – 0) y – 2 = 2/3x 3y – 6 = 2x --------------- (1) Now put (-3,0) in equation (1), i.e. x = -3 and y = 0; – 6 = – 6 Hence (-3,0) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Now checking other points, whether it satisfies the equation of line or not. putting (-2,-3) in equation (1); - 9 - 6 = - 4 (-2,-3) does not lie on the line. Putting (2,5) in equation (1); 15 – 6 = 4 (2,5) does not lie on the line. Putting (3,4) in equation (1); 12 – 6 = 6 6 = 6 Hence (3,4) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line. Putting (6,6) in equation (1); 18 – 6 = 12 12 = 12 Hence (6,6) lie on the line, as it satisfies the equation of line, so vera can use (-3,0) to graph the line.e
Solutions just means the amount of times the lines intersect, so there are no solutions. Since the lines are parallel, they’re going the exact same direction forever and ever, never intersecting. Hope this helps!
