Answer: -3
Step-by-step explanation:
To find the value of \( d \) when the points \( (d, 8) \) and \( (-6, -10) \) fall on a line with a slope of 6, we can use the slope formula:
Given that the slope is 6 and the points are \( (d, 8) \) and \( (-6, -10) \), we can substitute the coordinates into the formula to solve for \( d \):
\[ 6 = \frac{{8 - (-10)}}{{d - (-6)}} \]
Simplify the expression:
\[ 6 = \frac{{8 + 10}}{{d + 6}} \]
-3\[ 6 = \frac{{18}}{{d + 6}} \]
Now, cross multiply:
\[ 6(d + 6) = 18 \]
\[ 6d + 36 = 18 \]
Subtract 36 from both sides:
\[ 6d = 18 - 36 \]
\[ 6d = -18 \]
Divide both sides by 6:
\[ d = \frac{{-18}}{{6}} \]
\[ d = -3 \]
So, the value of \( d \) is -3.
