y = 2/3x -6
Conditions for Lines to be parallel
If two straight lines are cut by a transversal, the pair of alternate angles are equal, then two straight lines are parallel to each other. the pair of interior angles on the same side of traversals is supplementary, then the two straight lines are parallel.
Given line
3y – 2x = – 2
passes through (3, –3)
The slope-intercept form is
y =mx+b,
where m is the slope and
b is the y-intercept.
y = mx+b
Divide each term in
3y – 2x = – 2 by -2 and simplify.
-3/2y +x =1
Reorder terms.
y = -(2/3)(x+1)
Using the slope-intercept form, the slope is
2/3.m=2/3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope
2/3 and a given point (3, –3)
to substitute for
x1 and y1
in the point-slope form
y−y1=m(x−x1)
which is derived from the slope equation
m=(y2−y1)x2−x1.
y−(-3)=2/3⋅(x−(3))
Simplify the equation and keep it in point-slope form.
y+4=2/3⋅(x-3)
y = 2/3x -6
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