The equations (2x) and (2y - x = 4) represent two lines in a Cartesian coordinate system. The equation (2x) is simply a vertical line at (x = 0), while the equation (2y - x = 4) can be rearranged to slope-intercept form as (y = \frac{1}{2}x + 2), indicating a line with a positive slope. Therefore, the first line is vertical, and the second line is slanted with a positive slope.
parallel
To determine the type of lines represented by the equations ( y = 2x + 4 ) and ( y = 2x + 5 ), we can observe their slopes. Both equations have the same slope of 2, indicating that they are parallel lines. Since parallel lines never intersect, they will never meet at any point on the graph.
The lines are mutually perpendicular.
2X + 5Y = 6 5Y = - 2X + 6 Y = - 2/5X + 6/5 ----------------------------------and 5X - 2Y = 8 2Y = - 5X + 8 Y = - 5/2 + 4 ------------------- Look like intersecting lines, though not perpendicular
At the point (2, 4).
If: 12 = 2y+x then y = -1/2x+6 So: y = 2x+4 and y = -1/2x+6 which means that they are perpendicular lines
parallel
They are straight lines.
If you mean: y = 2x and 2y = -x+4 then they are positive and negative straight line equations
To determine the type of lines represented by the equations ( y = 2x + 4 ) and ( y = 2x + 5 ), we can observe their slopes. Both equations have the same slope of 2, indicating that they are parallel lines. Since parallel lines never intersect, they will never meet at any point on the graph.
The lines are mutually perpendicular.
-2X + 2Y = 4 2Y = 2X + 4 Y = X +2 by inspection, 2 but, you could also 0 out X in original equation -2(0) + 2Y = 4 2Y = 4 Y = 2
At the point (2, 4).
2X + 5Y = 6 5Y = - 2X + 6 Y = - 2/5X + 6/5 ----------------------------------and 5X - 2Y = 8 2Y = - 5X + 8 Y = - 5/2 + 4 ------------------- Look like intersecting lines, though not perpendicular
-2x + 2y = 4 is equivalent to twice -2 + y = 2 which is the equation of a straight line.
Put in function form. - 2X + 2Y = 4 2Y = 2X + 4 Y = X + 2 -------------set to 0 X + 2 = 0 X = -2 --------------X intercept
4x + 2y = -8 → 2y = -4x - 8 → y = -2x - 4