Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
Two lines are parallel if they have equal slopes.
First line is in slope intercept form and has slope m. Now we have to find slope of the second line, m2. Write it in slope intercept form
So, slope of the second line is m2 = 2. This means that the lines will be parallel if m = 2.
Also, if lines are parallel, they may overlap giving us infinitely many solutions. We can check that by finding y−intercepts.
Intercept of first line is y1=−6 and intercept of second line is y2=−3, so lines do not overlap. Thus, for m=2 we have parallel lines with no solutions.