Question

How do you tell whether the lines for each pair of equations are parallel, perpendicular, or neither: `y=-4x+3, -2x+8y=5`?

Answer 1

`"lines are perpendicular"`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"express both equations in this form and consider their"`
`"slopes"`

`• " parallel lines have equal slopes"`

`• " the product of the slopes of perpendicular lines equals -1"`

`y=-4x+3larrcolor(blue)"is in slope-intercept form"`

`"with slope m "=-4`

`"rearranging "-2x+8y=5larrcolor(blue)"add 2x to both sides"`

`rArr8y=2x+5`

`"divide all terms by 8"`

`rArry=1/4x+5/8larrcolor(blue)"in slope-intercept form"`

`"with slope "=1/4`

`-4!=1/4" hence lines are not parallel"`

`-4xx1/4=-1" hence lines are perpendicular"`