The slopes of each pair when analyzed shows us that; first is parallel; second and third are perpendicular and fourth is neither.
How to find the Slope of a Line?
The general form of an equation in slope intercept form is;
y = mx + c
where m is the slope
1) The first pair shows that;
y = 6x/5 - 8/5
y = 6x/5 - 5
The slope in both cases is the same and so they are parallel.
2) The second pair of equations shows that;
y = (1/2)x + (1/2)
y = -2x - 5
Both slopes are negative reciprocals of each other and so they are perpendicular.
1st and 3rd box is for perpendicular
3) The third pair of equations shows that;
y = (5/7)x + (8/7)
y = -(7/5)x + 10
Both slopes are negative reciprocals of each other and so they are perpendicular.
1st and 3rd box is for perpendicular.
4) The third pair of equations shows that;
y = 2x + 5
y = 3x + 4
Both slopes are neither parallel nor perpendicular to each other.
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