Question

if the slope if it exist x+7y=14

Answer 1

if we solve for y and put in slope intercept form, we can see the slope more clearly:

x+7y=14 subtract x from both sides
7y=14-x divide by 7
\[y=-\frac{14-x}{7}\]
we can split this to two fractions
\[y=-\frac{14}{7}+\frac{x}{7}\]
simplifying and rearranging to y=mx+b form:
\[y=\frac{1}{7}x-2\]
so our slope is 1/7

Answer 2

Slope would be -1/7 not 1/7, in the second step you wrote,
\[y=-(14-x)/7\] instead of \[y=(14-x)/7\]