Question

The equations of four lines are given. Identify which lines are parallel.

Line 1: y=−3/4x−6
Line 2: y−7=−4(x+9)
Line 3: y=−2x+6
Line 4: x+4/3y=−5

Answer 1

`$$Lines \textbf{1} and \textbf{4} are parallel.`

Explanation:

`$$We know that parallel lines have the same slope. To determine which lines are parallel, we simply need to determine their slopes. We can do this by putting the equations in standard form\begin{center}$y=mx+b$\end{center} where $m$ is equal to the slope, and $b$ is equal to the y-intercept.\\Line 1: This line is already in standard form. The slope is $-(3)/(4)$.\\Line 2: Isolate $y$ to obtain standard form:\begin{center}$y-7=-4(x+9)\\\Rightarrow y=-4(x+9)+7\\\Rightarrow y=-4x-29$\end{center}\\`

`$$We can see that the slope of line 2 is -4.\\Line 3: This line is already in standard form. The slope is $-2$.\\Line 4: Isolate $y$ to obtain standard form:\begin{center}$x+(4/3)y=-5\\\Rightarrow(4/3)y=-x-5\\\Rightarrow y=-(x)/((4)/(3))-(5)/((4)/(3))\\\Rightarrow y=-(3)/(4)x-(15)/(4)$\end{center}We can see that the slope of line 4 is $-(3)/(4)$. \\Lines 1 and 4 both have slopes of $-(3)/(4)$. Hence, lines \textbf{1} and \textbf{4} are parallel.`