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)

Question
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.

Relevant Questions

The parallel lines at the right are cut by a transversal. Find the value of x.
a. Angles 1 and 2 are corresponding angles, $$\displaystyle{m}∠{1}={45}°$$, and $$\displaystyle{m}∠{2}={\left({x}+{25}\right)}°$$.
b. Angles 3 and 4 are alternate interior angles, $$\displaystyle{m}∠{3}={2}{x}°$$, and $$\displaystyle{m}∠{4}={80}°$$.
Give the equation of the line perpendicular to the line described and satisfying the given conditions. $$\displaystyle{y}=-{\left(\frac{{4}}{{3}}\right)}{x}+{5}$$ with y-intercept (0, -8)
A line passes through the point (2, 1) and has a slope of $$\frac{-3}{5}$$.
What is an equation of the line?
A.$$y-1=\frac{-3}{5}(x-2)$$
B.$$y-1=\frac{-5}{3}(x-2)$$
C.$$y-2=\frac{-3}{5}(x-1)$$
D.$$y-2=\frac{-5}{3}(x-1)$$
Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3
Write the equation of a line perpendicular to $$\displaystyle{y}=\frac{{1}}{{4}}{x}-{5}$$ that passes through the point (-1,2)
through: (3, 0), parallel to y= -4
Simplify each expression.
1. -n+9n+3-8-8n
2. 3(-4x+5y)-3x(2+4)
5. 5-4y+x+9y
7. -2x+3y-5x-(-8y)
We give linear equations. For each equation,
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
y=−1+2x