Question

How do you find the slope that is perpendicular to the line `7x+2y=3`?

Answer 1

`color(brown)("Slope f the perpendicular line "color(indigo)(m_1 = -(1 / m) = 2/7`

Explanation:

`7x + 2y = 3`

Standard form of slope intercept equation is `y = mx + c` where m is the slope.

`2y = -7x + 3`

`y = -(7/2)x + 3/2`

Slope of the given line `m = -(7/2)`

Slope f the perpendicular line `m_1 = -(1 / m) = -(1 / (-7/2)) = 2/7`

Answer 2

`"perpendicular slope "=2/7`

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"`

`"rearrange "7x+2y=3" into this form"`

`"subtract 7x from both sides"`

`cancel(7x)cancel(-7x)+2y=-7x+3`

`rArr2y=-7x+3`

`"divide all terms by 2"`

`rArry=-7/2x+3/2larrcolor(red)"in slope-intercept form"`

`"with slope m "=-7/2`

`"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`

`rArrm_("perpendicular")=-1/(-7/2)=2/7`