Answer:
Step-by-step explanation:
To write the equation of the line passing through the points \((3, 1)\) and \((5, 4)\) in slope-intercept form (\(y = mx + b\)) and function notation (\(f(x) = mx + b\)), we first need to find the slope (\(m\)) of the line using the formula:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the given points. After finding the slope, we can use one of the points to find the \(y\)-intercept (\(b\)) by solving for \(b\) in the slope-intercept form equation. Let's calculate the slope and \(y\)-intercept.
The slope (\(m\)) of the line is \(1.5\), and the \(y\)-intercept (\(b\)) is \(-3.5\). Therefore, the equation of the line in slope-intercept form is:
\[y = 1.5x - 3.5\]
In function notation, this can be written as:
\[f(x) = 1.5x - 3.5\]
