Question

which value of m will create a system of parallel lines with no solution?
y = mx - 6
8x - 4y = 12
options: \\(\frac{1}{2}\\), 2, -2, \\(-\frac{1}{2}\\)

Explanation:

Step1: Rewrite the second equation in slope - intercept form

The slope - intercept form of a line is $y = kx + b$, where $k$ is the slope and $b$ is the y - intercept. We start with the equation $8x-4y = 12$.
First, we isolate $y$:
Subtract $8x$ from both sides: $-4y=-8x + 12$.
Then divide each term by $-4$: $y=\frac{-8x}{-4}+\frac{12}{-4}$, which simplifies to $y = 2x-3$.

Step2: Determine the slope for parallel lines

For two lines to be parallel, their slopes must be equal. The first line is given by $y=mx - 6$, and its slope is $m$. The second line, $y = 2x-3$, has a slope of $2$.
So, for the lines $y = mx-6$ and $y = 2x - 3$ to be parallel (and thus have no solution, since parallel lines never intersect), the slope $m$ must be equal to $2$.

Answer:

2