Question

Determine if the lines are parallel, perpendicular, or neither. Line 1: y-x=3 Line 2: x+y=-5

Answer 1

lines are perpendicular

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

y - x = 3 ( add x to both sides )

y = x + 3 ← in slope- intercept form

with slope m = 1

line 2

x + y = 5 ( subtract x from both sides )

y = - x + 5 ← in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes

clearly the lines are not parallel

• the product of the slopes of perpendicular lines = - 1

1 × - 1 = - 1

then the 2 lines are perpendicular to each other

Answer 2

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The given equations are

y - x = 3

x + y = -5

We would make both equations to look like the slope intercept equation. We have

For y - x = 3,

Adding x to both sides of the equation, we have

y - x + x = 3 + x

y = x + 3

The slope is 1

For x + y = - 5,

Subtracting x from both sides of the equation, we have

x - x + y = - 5 - x

y = - x - 5

The slope is - 1

Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. We know that 1 is the - 1

Thus, the lines are perpendicular