Find equations of the lines that pass through (-5, 7) and are (a) parallel to, and (b) perpendicular to the line 2x−y=−3

Answer 1

ax + by = c is general form of the equation of a line. slope = -a/b

so for line 2x-y = -3, slope = -2/-1 = 2

slope of line parallel to it has the same slope 2

point-intercept form of line = y - y1 = m(x - x1), where (x1,y1) is a point on the line

here m = 2 and (x1,y1) is (-5,7), so

y - 7 = 2(x+5)

y - 7 = 2x + 10

2x -y = -17

slope of line perpendicular to it has the slope that is negative reciprocal of 2 = -1/2

point-intercept form of line = y - y1 = m(x - x1), where (x1,y1) is a point on the line

here m = -1/2 and (x1,y1) is (-5,7), so

y - 7 = -1/2(x+5)

2y - 14 = -(x+5)

2y - 14 = -x - 5

x + 2y = 9