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

##### 2 Answers

#### Explanation:

First, convert

The perpendicular line to

The new line will be

We know that it passes through

So, the new equation of the line will be

#### Explanation:

#"given a line with slope m then the slope of a line "#

#"perpendicular to it is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#"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"#

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

#rArr-5y=-10x+8rArry=2x-8/5rArrm=2#

#rArrm_(color(red)"perpendicular")=-1/2#

#rArry=-1/2x+blarrcolor(blue)"is the partial equation"#

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

#4=-1+brArrb=4+1=5#

#rArry=-1/2x+5larrcolor(red)"perpendicular equation"#