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Which value of m will create a system of parallel lines with no solution?

y=mx-6

8x-4y=12

A coordinate grid with one line labeled 8 x minus 4 y equals 12. The line passes through a point at (0, negative 3), (1, negative 1) and a point at (1.5, 0).

-2
-

2

1 answer

To determine the value of \( m \) that will create a system of parallel lines with no solution, we need to analyze the given equations:

  1. The first equation is given in slope-intercept form: \[ y = mx - 6 \] Here, the slope of this line is \( m \).

  2. The second equation, \( 8x - 4y = 12 \), can be rearranged into slope-intercept form (\( y = mx + b \)) by solving for \( y \): \[ 8x - 4y = 12 \ -4y = -8x + 12 \ y = 2x - 3 \] Now, we can see that the slope of this line is \( 2 \).

For the two lines to be parallel, their slopes must be equal. Therefore, we set the slope from the first equation equal to the slope from the second equation: \[ m = 2 \]

Thus, the value of \( m \) that will create a system of parallel lines with no solution is: \[ \boxed{2} \]