Question

# 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

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

2020-10-24

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.