How do you write an equation of a line passing through (2, 4), perpendicular to 10x - 5y = 810x−5y=8?

2 Answers
Nam D.
Jan 8, 2018

y=-1/2x+5y=−12x+5

Explanation:

First, convert 10x-5y=810x−5y=8 into the form of y=mx+by=mx+b

10x-5y=810x−5y=8

-5y=8-10x−5y=8−10x

y=2x-8/5y=2x−85

The perpendicular line to y=2x-8/5y=2x−85 will have a slope equal to -1/2−12, because perpendicular lines' slopes have a product of -1−1.

The new line will be

y=-1/2x+by=−12x+b

We know that it passes through (2,4)(2,4), so we can plug that into the new equation.

4=-1/2*2+b4=−12⋅2+b

4=-2+b4=−2+b

b=6b=6

So, the new equation of the line will be

y=-1/2x+5y=−12x+5

Jim G.
Jan 8, 2018

y=-1/2x+5y=−12x+5

Explanation:

"given a line with slope m then the slope of a line "given a line with slope m then the slope of a line
"perpendicular to it is"perpendicular to it is

•color(white)(x)m_(color(red)"perpendicular")=-1/m∙xmperpendicular=−1m

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

•color(white)(x)y=mx+b∙xy=mx+b

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

"rearrange "10x-5y=8" into this form"rearrange 10x−5y=8 into this form

rArr-5y=-10x+8rArry=2x-8/5rArrm=2⇒−5y=−10x+8⇒y=2x−85⇒m=2

rArrm_(color(red)"perpendicular")=-1/2⇒mperpendicular=−12

rArry=-1/2x+blarrcolor(blue)"is the partial equation"⇒y=−12x+b←is the partial equation

"to find b substitute "(2,4)" into the partial equation"to find b substitute (2,4) into the partial equation

4=-1+brArrb=4+1=54=−1+b⇒b=4+1=5

rArry=-1/2x+5larrcolor(red)"perpendicular equation"⇒y=−12x+5←perpendicular equation

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