Y=16-5x
Y=1/2x-9
Y=3x
Y=10
Need to write a parallel equation, perpendicular equation and neither parallel nor perpendicular line for all of them, please help
Put them in the form y = m x + b
for example with the first one:
y = -5 x + 16
here m - -5 and b = 16
now parallel just has same slope m
y = -5 x + 16,529
or any other b
perpendicular means m' = -1m
so here +1/5
y = (1/5) x + 16437 or whatever
neight means m = 5735.787
so
y = 5735.787 x + anything
or whatever
now y = 3 x
y = 3 x + anything is parallel
y = (-1/3)x + anything is pependicular
etc
To find the parallel and perpendicular equations for the given lines, we need to determine their slopes. The slope-intercept form of a linear equation is given as y = mx + b, where m is the slope and b is the y-intercept.
1) Line equation: Y = 16 - 5x
Slope (m) = -5
This line does not have a y-intercept since the constant term is 16.
Parallel equation: To find a parallel line, we need to have the same slope, but a different y-intercept. Let's say the new y-intercept is c.
Parallel equation: Y = -5x + c
Perpendicular equation: To find a perpendicular line, we need to have a negative reciprocal slope. The negative reciprocal of -5 is 1/5. Let's assume the new y-intercept is d.
Perpendicular equation: Y = 1/5x + d
2) Line equation: Y = 1/2x - 9
Slope (m) = 1/2
Y-intercept (b) = -9
Parallel equation: Parallel lines have the same slope and different y-intercepts. Let's assume the new y-intercept is e.
Parallel equation: Y = 1/2x + e
Perpendicular equation: Perpendicular lines have a negative reciprocal slope. The negative reciprocal of 1/2 is -2. Assume the new y-intercept is f.
Perpendicular equation: Y = -2x + f
3) Line equation: Y = 3x
Slope (m) = 3
Y-intercept (b) = 0 (since there is no constant term)
Parallel equation: Parallel lines have the same slope and different y-intercepts. Let's say the new y-intercept is g.
Parallel equation: Y = 3x + g
Perpendicular equation: Perpendicular lines have a negative reciprocal slope. The negative reciprocal of 3 is -1/3. Let's assume the new y-intercept is h.
Perpendicular equation: Y = -1/3x + h
4) Line equation: Y = 10
This equation represents a horizontal line since the slope is 0.
Any equation with a different y-intercept will be parallel to this line.
For example: Y = 5, Y = -2, etc.
Since the given line is horizontal, it does not have a perpendicular line, as a perpendicular line to a horizontal line would be vertical.
In summary:
1) Y = 16 - 5x
Parallel equation: Y = -5x + c
Perpendicular equation: Y = 1/5x + d
2) Y = 1/2x - 9
Parallel equation: Y = 1/2x + e
Perpendicular equation: Y = -2x + f
3) Y = 3x
Parallel equation: Y = 3x + g
Perpendicular equation: Y = -1/3x + h
4) Y = 10
Any equation with a different y-intercept is parallel. No perpendicular lines exist since the given line is horizontal.