Final answer:
Using the slope formula, the value of x for a line passing through the points (5,3) and (x,9) with a slope of 3/5 is found to be 15.
Step-by-step explanation:
To find the value of x for the point (x,9) on a line with a slope of 3/5, we can use the slope formula:
Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Given the slope is 3/5, and the line goes through points (5,3) and (x,9), we can substitute into the slope formula:
3/5 = (9 - 3) / (x - 5)
3/5 = 6 / (x - 5)
Now we cross multiply to solve for x:
3*(x - 5) = 5*6
3x - 15 = 30
3x = 30 + 15
3x = 45
x = 45 / 3
x = 15
Therefore, the value of x is 15.