Question 250242
convert the equation to slope-intercept form.


the slope-intercept form of a straight line is y = mx + b where m is the slope and b is the y-intercept.


2x + 4y = 9 is the equation.


subtract 4x from both sides of the equation to get:


4y = -2x + 9


divide both sides of the equation by 4 to get:


y = (-2/4)x + (9/4)


that's the slope intercept of the line.


the slope is (-2/4) which is the same as (-1/2).


the equation becomes:


y = (-1/2)x + (9/4)


the line parallel to this line will have the same slope.


the equation for that line starts out as:


y = (-1/2)x + b


take your point of (x,y) = (6,-2) and substitute for x and y in this equation to get:


-2 = (-1/2)*6 + b


simplify to get:


-2 = -3 + b


add 3 to both sides of this equation to get:


-2 + 3 = b


combine like terms to get:


1 = b


equation of line parallel to your line is:


y = (-1/2)x + 1


you have 2 equations that are parallel to each other.


those equations are:


y = (-1/2)x + (9/4) and y = (-1/2)x + 1


graph of the equations of these lines is shown below:


{{{graph (600,600,-10,10,-10,10,(-1/2)x  + (9/4),(-1/2)x + 1)}}}


you can see that the equation of y = (-1/2)x + (9/4) crosses the y-axis at about y = 2.25 which is where it would cross when x = 0.


you can see that the equation of y = (-1/2)x + 1 crosses the y-axis at about y = 1 which is where it would cross when x = 0.


you can see that the equation of y = (-1/2)x + 1 goes through the point (x,y) = (6,-2).