Question

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

Answer 1

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:
\[
\boxed{2}
\]