Explanation:
A and C are parallel. equations G and E.
B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.
parallel means that both lines have the same slope.
the slope is the factor a of x when the equations look like
y = ax + b (slope-intercept form)
or
y - y1 = a(x - x1) (point-slope form)
"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.
the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.
the perpendicular slope to y/x is the upside down ratio and the sign is flipped.
e.g. the perpendicular slope to 5/4 is -4/5.
equation E is already in point-slope form.
the slope is 2/3, and the point (-9, -2) must be on the line.
only one line goes through the point (-9, -2) : C.
equation H is already in slope-intercept form.
the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).
only one line goes through that point : D
equation F
2x + 3y = -21
3y = -2x -21
y = (-2/3)×x - 7
the slope is -2/3, which is perpendicular to 3/2 (equation H).
the y-intercept is -7, meaning the line goes through the point (0, -7).
only one line goes through that point : B
equation G
-2x + 3y = -6
3y = 2x - 6
y = (2/3)×x - 2
the slope is 2/3 (parallel to equation E).
the y-intercept is -2, meaning the line goes through the point (0, -2).
only one line goes through that point : A