Identify the lines that are parallel.Line 1: y=−5Line 2: 4y−16x=−1Line 3: x=−6Line 4: y+5=4(x+1)

Linear equations and graphs
asked 2020-10-23

Identify the lines that are parallel.
Line 1: \(y=−5\)
Line 2: \(4y−16x=−1\)
Line 3: \(x=−6\)
Line 4: \(y+5=4(x+1)\)

Answers (1)


Parallel lines are line that have same slope, where \(m1 = m2\). To identify what line are parallel to each other, convert the equation into \(y=mx+b\) and get the slope of each equation.
Line 1, \(y=mx+b\)
\(y=0x-5\) , where the slope of line 1 is \(m1=0\)
Line 2, \(y=mx+b\)
\(4y−16x=−1\) , simplifying the equation by multiplying it by \(\displaystyle\frac{{1}}{{4}}\) will result to \(\displaystyle{y}={4}{x}-\frac{{1}}{{4}}\), where the slope of the line 2 is \(m2=4\)
Line 3, \(x=-6\) , since the graph of the line 3 is vertical its slope is undefined.
Line 4, \(y=mx+b\)
\(y+5=4(x+1) y=4x-4\) , where the slope of line 4 is also \(m4=4\). Therefore, based on the slopes of the given equations, we can say that line 2 and line 4 is parallel to each other.

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