Postulates:
• Parallel lines have the same slope, but different y-intercepts, because they start at different locations and stay the same slope next to each other for infinity.
• Perpendicular Lines have a negative reciprocal slope of the original line’s slope.
Solving:
We want the lines to be in slope l-intercept form: y=mx+b to determine the slope and y-intercept.
Line a: 3x+y=7 —> 3x-3x+y=7-3x —> y=-3x+7
Line b: 6x+2y=-8 —> 6x-6x+2y=-8-6x —> 2y=-6x-8 —> 2y/2=-6/2x+8/2 —> y=-3x+4
Line c: -x+3y=6 —> -x+x+3y=x+6 —> 3y/3=x/3+6/3–> y=1x/3+2.
Line a and b have the same slope of -3x with different y-intercepts; therefore, they are PARALLEL.
Line c has a different slope than lines a and b, so it is not parallel. Let’s see if it’s perpendicular to lines a and c.
Perpendicular lines have a negative reciprocal slope from the original line. Here’s the formula: y=x/z+b ——> y=-z/x+b
Line a: y=-3x+y
Line b: y=-3x+4
Line c: y=1x/3+2.
Let’s plug line a into the formula to see if the result is the slope of line c:
y=x/3+2 ——> y=-3/x+2.
Therefore, lines a and b are PERPENDICULAR to line c.
Feel free to give Brainliest!
