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)

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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