Question

Give the slope-intercept form of the equation of the line that is perpendicular to 7x+3y=18 and contains P(6,8)

With the explanation please :) ​

Answer 1

`y = (3)/(7)x + 5 (3)/(7)`

Explanation:

Slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

Given equation: 7x +3y= 18

Rewrite into slope-intercept form to find out its gradient:

7x +3y= 18

3y= -7x +18

`y = - (7)/(3) x + 6`

Thus, gradient of given line is -7/3.

The product of the gradients of 2 perpendicular lines is -1.

(Gradient of line)(-7/3)= -1

Gradient of line

`= - 1 / ( - (7)/(3)) \\ = - 1 *( - (3)/(7) ) \\ = (3)/(7)`

Substitute m= 3/7 into the equation:

`y = (3)/(7)x + c`

To find the value of c, substitute a pair of coordinates.

Since the line contains P(6,8), we substitute x=6 and y=8 into the equation.

When x=6, y= 8,

`8 = (3)/(7) (6) + c \\ c = 8 - (18)/(7) \\ c = 5 (3)/(7)`

Thus, the equation of the line is
`y = (3)/(7) x + 5 (3)/(7)`.