which value of m will create a system of parallel lines with no solution?\ny = mx - 6\n8x - 4y = 12
which value of m will create a system of parallel lines with no solution?\ny = mx - 6\n8x - 4y = 12
Answer
Explanation:
Step1: Rewrite the second - line equation in slope - intercept form
We have $8x - 4y=12$. Solve for $y$: [ \begin{align*} -4y&=-8x + 12\ y& = 2x-3 \end{align*} ] The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the line $y = 2x-3$, the slope $m_1 = 2$.
Step2: Determine the value of $m$ for parallel lines
Two lines $y=m_1x + b_1$ and $y=m_2x + b_2$ are parallel if $m_1=m_2$. The first line is $y=mx - 6$. Since it should be parallel to $y = 2x-3$, then $m = 2$.
Answer:
$m = 2$