Question

What is the equation of the line in slope-intercept form that passes through the point (–2, 4) and is perpendicular to the line y = –2x + 4?

Answer 1

`y=1/2x+5`

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"`

`y=-2x+4" is in this form"`

`rArrm=-2" and "m_(color(red)"perpendicular")=-1/(-2)=1/2`

`rArry=1/2x+blarr" partial equation"`

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

`4=-1+brArrb=4+1=5`

`rArry=1/2x+5larrcolor(red)" in slope-intercept form"`