Answer:
[tex]y = \frac{3}{7}x + 5 \frac{3}{7} [/tex]
Step-by-step 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
[tex]y = - \frac{7}{3} x + 6[/tex]
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
[tex] = - 1 \div ( - \frac{7}{3}) \\ = - 1 \times( - \frac{3}{7} ) \\ = \frac{3}{7} [/tex]
Substitute m= 3/7 into the equation:
[tex]y = \frac{3}{7}x + c [/tex]
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,
[tex]8 = \frac{3}{7} (6) + c \\ c = 8 - \frac{18}{7} \\ c = 5 \frac{3}{7} [/tex]
Thus, the equation of the line is [tex]y = \frac{3}{7} x + 5 \frac{3}{7} [/tex].
