# How do you find a standard form equation for the line with #(7,-4)# and perpendicular to the line whose equation is #x-7y-4=0#?

##### 2 Answers

#### Explanation:

#"the equation of a line in "color(blue)"standard form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#

where A is a positive integer and B, C are integers.

#• " 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#

#"rearrange "x-7y-4=0" into "color(blue)"slope-intercept form"#

#•color(white)(x)y=mx+b#

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

#rArry=1/7x-4/7rArrm=1/7#

#rArrm_(color(red)"perpendicular")=-1/(1/7)=-7#

#rArry=-7x+blarr" partial equation"#

#"to find b substitute "(7,-4)" into the partial equation"#

#-4=-49+brArrb=45#

#rArry=-7x+45larrcolor(red)" in slope-intercept form"#

#rArr7x+y=45larrcolor(red)" in standard form"#

#### Explanation:

The given equation is in standard form which is

but we need to know its slope, so change it into the form

If lines are perpendicular then

(One slope is the negative reciprocal of the other - flip and change the sign.)

The slope perpendicular to

Now we have a point