Write an equation for the line described. Write the equation in the form specified. Parallel to x=6, through (1,3)

All vertical lines are parallel so:
x=1

graph the following system of equations using slope and y intercept determine the number of solutions for the system, 2x+3y=6 and 4x+6y=24

 
these two lines clearly have the same slope yet they have different y-intercepts, so they must be parallel. Therefore the number of solutions is 0 

If a line has a gradient of 5/2 what will the gradient be of a perpendicular line be if a line has a gradient of 5/2? What will the gradient be of a parallel line be?

The slopes of perpendicular lines have a product of -1. So can write: 

 

Parallel lines have the same slope: 

Find the equation for that is parallel to the line with the equation y=-3 passing through the point (-1,-1)

y=-3 is a horizontal line - therefore the other line is also horizontal: 


y=-1

Find the equation for the line that passes through the point (2,4), and that is parallel to the line with the equation y=1/2×-3/2

Slopes are the same because they are parallel.
Point-Slope form:

Consistent or not: x-3y=4,4x-12y=6 ?

not consistent - these lines are parallel: 

D4: 4x-12y=6 
yields x-3y=2/3 
so they have the same slope, but different y-intercepts 

:)

Determine if the graphs of the given equations are parellel. y=2x+6 5y+2x=4

these are not parallel because one has a slope of m=2 and the other has a slope of m=-5/2 (parallel lines have the same slope)

is 9x+3y=12; 27x+9y=40 parallel, perpendicular, or neither?

We know that two lines are parallel if they have the same slope (and they are distinct). When the lines are in general form we'll use the formula m=-B/A to find their slopes with 
 

 


first line: m=-3/9=-1/3 
second line: m=-9/27=-1/3 

these lines have the same slope and since we know that they are not the same line because 
 


they must be parallel 

:)

For the pair of equations, determine whether their graphs are parallel, perpendicular, or neither.

Solution:

The slopes of two parallel lines are equal so these lines are not parallel. the product of perpendicular lines is -1. The product of these slopes is: 
(2)(-1/2)=-1 
Therefore these lines are perpendicular

Find the equation of the line parallel to y=3x+1 and passing through point P(2,5)

Equations of lines