Final answer:
To find the value of x for a line with a slope of 2/3 passing through (-6, 0) and (x, 6), we use the slope formula and calculate that x = 3.
Step-by-step explanation:
To find the value of x for which a line with a slope of 2/3 passes through the points (-6, 0) and (x, 6), we can use the slope formula:
slope (m) = (y2 - y1) / (x2 - x1)
Substituting the given values into the formula:
(6 - 0) / (x - (-6)) = 2/3
After simplifying, we have:
6 / (x + 6) = 2/3
Cross-multiplying gives:
3 × 6 = 2 × (x + 6)
18 = 2x + 12
Subtracting 12 from both sides:
6 = 2x
Dividing by 2:
x = 3
Hence, the value of x is 3.