Final answer:
The value of g for the line with a slope of 4 passing through the points (3, 1) and (5, g) is 9, as calculated using the slope formula. The correct answer is option c. 9.
Step-by-step explanation:
To find the value of g where a line with a slope of 4 passes through the points (3, 1) and (5, g), you can use the formula for the slope of a straight line, which is (change in y) / (change in x). In this case, since the slope m is 4, the formula will look like this:
(g - 1) / (5 - 3) = 4
This simplifies to:
(g - 1) / 2 = 4
Multiplying both sides by 2 gives you:
g - 1 = 8
Adding 1 to both sides gives you the value of g:
g = 9
Therefore, the value of g where the line with a slope of 4 passes through the points (3,1) and (5,g) is 9.