Question 226400
slope-intercept form of the equation of a line is y = mx = b where m is the slope and b is the y-intercept.


equation of 2x + 2y = 6 is the standard form of the equation of a line.


That standard form is ax + by = c


You need to convert that equation to the slope intercept form first.


2x + 2y = 6 is the original equation.
subtract 2x from both sides of the equation to get:
2y = -2x + 6
divide both sides of the equation by 2 to get:
y = -x + 3


your original equation in slope-intercept form is:


y = -x + 3


The slope of your original equation is -1.


Your equation will have the same slope.


take the general slope-intercept form of:


y = mx + b


and replace m with -1 to get:


y = -x + b


now take your points of (x,y) = (.9,.3) and replace x and y in this equation with them.


you get:


y = -x + b becomes:
.3 = -.9 + b
add .9 from both sides of this equation to get:
.3 + .9 = b
simplify to get:
b = 1.2


replace b in the slope-intercept form of your equation to get:


y = -x + 1.2


That should be your equation.


Graph the original equation and your equation to show as follows:


{{{graph(600,600,-4,4,-4,4,-x+3,-x+1.2,.9)}}}


The horizontal line at y = .9 shows you that this occurs on your parallel line at around x = .3