Question

If line a is perpendicular to line b and the slope of line a is 7 whats the slope of line b

Answer 1

Answer: "
`-(1)/(7)` " .

_____________

Explanation:

Assume we have a two-dimension Cartesian plane graph;

in which equations of straight lines can be expressed in the form of:
" y = mx + b " ;

in which:

"m" is the slope; as well as the "coefficient" of "x" ;
and: "b" is the y-intercept; that is, the value "y" value of the "(x, y)" coordinate at the point which "x = 0" ; that is, where the graph crosses the "y-axis".

Given the ^aformentioned conditions:
Note that if we select a line that can be written in the format:
" y = mx + b " ; then another line that is "perpendicular" to that
[selected line] will have the slope, "m"; of the value that is the "negative reciprocal value" of the slope, "m" ; of the other line.

Note that is our problem, we select a line—in our given problem:
"Line a" —with a slope, "m = 7 " ;
which is perpendicular to the slope of "Line b" ;
→ then: the slope of "Line B" ; would be the "negative reciprocal value"

of "7" .

Note: "
`7 = (7)/(1)` " ; the recriprocal would be: "
`-(1)/(7)` " .

_____________

Hope this answer is helpful to you!

Answer 2

If a line is perpendicular to another line, that means that the slope is completely opposite that of the original line. The first thing that we do to the slope is we negate the number which means that if we have a slope of
`-7` our slope because
`7` in this step. In our case our slope is
`7` so in this step it becomes
`-7`.

Moving onto the second part which is to get the reciprocal of the number which means that if we have
`(1)/(2)` then we would switch it to
`2`. In our case our number is
`-7` so we would make that into a fraction like this
`-(1)/(7)`.

In conclusion, our final slope of the perpendicular line is
`-(1)/(7)`.

Hope this helps! Let me know if you have any questions