Final answer:
To find the value of x for a line with points (x,2) and (-4,-6) and slope m = -4/5, use the slope formula and algebraic manipulation to solve for x, resulting in x = -14.
Step-by-step explanation:
To determine the value of x so that a line through points with the given coordinates (x,2) and (-4,-6) has the given slope m = -4/5, use the slope formula:
m = (Y₂ - Y₁) / (X₂ - X₁)
Substituting the known values, the equation becomes:
-4/5 = (2 - (-6)) / (x - (-4))
Which simplifies to:
-4/5 = (2 + 6) / (x + 4)
Then multiply both sides by (x + 4) to get:
-4/5(x + 4) = 8
Now distribute the left side and solve for x:
-4/5x - 16/5 = 8
Finally, multiply by 5 and add 16 to isolate x:
-4x - 16 = 40
-4x = 56
x = -14
The value of x that satisfies the given slope is -14.