If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?
Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
If you want to learn more about linear equations:
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