Determine is the solution set for the system of equations shown is the empty set contains one point or is infinite X+2y=0; 2x+4y
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Given:
The equation of a line is
Line v passes through point (6,6) and it is perpendicular to the given line.
Line w passes through point (-6,10) and it is parallel to the line v.
To find:
The equation in slope intercept form of line w.
Solution:
Slope intercept form of a line is
...(i)
where, m is slope and b is y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
So, slope of given line is .
Product of slopes of two perpendicular lines is -1.
Line w is perpendicular to the given line. So, the slope of line w is .
Slopes of parallel line are equal.
Line v is parallel to line w. So, slope of line v is also .
Slope of line v is and it passes thorugh (-6,10). So, the equation of line v is
where, m is slope.
Adding 10 on both sides, we get
Therefore the equation of line v is .