The linear function passing through points (3,6) and (1,0) has a slope of 3 and a y-intercept of -3. The correct equation representing the line is \(y - 3 = 3(x - 2)\) (option d).
To find the equation of a linear function given two points (x₁, y₁) and (x₂, y₂), you can use the slope-intercept form: \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
First, calculate the slope (\(m\)):
\[m = \frac{y₂ - y₁}{x₂ - x₁}\]
Let's use points (3,6) and (1,0):
\[m = \frac{0 - 6}{1 - 3} = \frac{-6}{-2} = 3\]
Now that we have the slope (\(m\)), we can use it with one of the points to find the y-intercept (\(b\)). Let's use (3,6):
\[6 = 3(3) + b \implies b = -3\]
The equation of the line is:
\[y = 3x - 3\]
Now, compare this with the given options:
a. \(y + 6 = -3(x + 1)\) - Not equivalent.
b. \(y - 6 = -3(x - 1)\) - Not equivalent.
c. \(y + 3 = 3(x + 2)\) - Not equivalent.
d. \(y - 3 = 3(x - 2)\) - This matches the derived equation.
Therefore, the correct answer is d. \(y - 3 = 3(x - 2)\).