Question

find the equation of the line that passes through the point(4,6) and the x intercept of 3x-2y +9=0
by the way i need explanation and working out
thank you!

Answer 1

you need the find the x-intercept of
\[3x-2y+9=0\] and then you will have two points with which to find the equation of the line

Answer 2

to find it set y = 0 and solve
\[3x+9=0\]
\[3x=-9\]
\[x=-3\] so the x-intercept is (-3,0)

Answer 3

now you have two points (-3,0) and (4,6)
the slope is
\[\frac{6-0}{4-(-3)}=\frac{6}{7}\]

Answer 4

use the point - slope formula to find the equation of the line:
\[y-y_1=m(x-x_1)\]

\[y-0=\frac{6}{7}(x-(-3))\]
\[y = \frac{6}{7}x+\frac{18}{7}\]

Answer 5

thank you! the answer provided was 7y=6x+18 which is the same
it all makes sense now! ^^