Prove whether the lines are parallel, perpendicular, or neither. Show your work and explain your reasoning. x + y = 1 and 4x + 4y = 1

Answer 1

x+y=1

4x+4y =1

multiply the 1st by 4 to get

4x+4y =4

they are two parallel lines, with the same slope

graph them, and they never intersect. parallel lines never intersect

or solve each equation for y to get

y=-x+1

and

y=-x +1/4

the coefficient of the x term is the slope

if slopes are the same, they are parallel lines

Answer 2

Recall that slope-intercept form of the equation of a line: y = mx + b. The m in the equation is the slope of the line. Rewrite x + y = 1 and 4x + 4y = 1 as y = -x + 1 and y = -x + 1/4, respectively, to see that the slopes of these lines are the same, -1. Therefore the lines are parallel.