Question

Write the equation of a line that is perpendicular to 2x-7y=13 and which passes through the point ( -3,8).

Answer 1

j

Explanation:

m

Answer 2

Given parameters:

Equation of the line given 2x - 7y = 13

Coordinates of points = -3, 8

Unknown:

Equation of a line perpendicular = ?

Solution;

To find the equation of this line, simply find the negative inverse of the given line.

m =
`-(1)/(m)`

2x - 7y = 13 , this is an equation of a straight line

let us write it in the form y = mx + c so as to derive the slope

y and x are coordinates

m is the slope

c is the y intercept

2x - 7y = 13;

-7y = -2x + 13

divide through by -7;

y =
`(2)/(7)x` +
`(13)/(7)`

The slope of this line is
`(2)/(7)`;

Now the slope of a line perpendicular to it will be
`-(7)/(2)`;

the equation of the line will be;

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

Since the coordinate of this line is (-3,8) , let us find C;

y = 8 and x = -3;

8 =
`-(7)/(2)` (-3) + C

multiply through by 2;

16 = 21 + 2C

16 - 21 = 2C

-5 = 2C

C =
`(-5)/(2)`

Now the equation of the line is;

y =
`-(7)/(2) x + (5)/(2)`