Questions: Write an equation for a linear function given a graph of (f(x)) shown below. (f(x)=square)

Solution Steps

Two points that lie on the line are \((0, -1)\) and \((1, 3)\).

The slope of the line is given by \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((0, -1)\) and \((1, 3)\), we have \[ m = \frac{3 - (-1)}{1 - 0} = \frac{4}{1} = 4 \]

The y-intercept is the point where the line crosses the y-axis. From the graph, this occurs at \((0, -1)\), so the y-intercept is \(-1\).

The slope-intercept form of a linear equation is given by \[ y = mx + b \] where \(m\) is the slope and \(b\) is the y-intercept. In this case, the slope is \(4\) and the y-intercept is \(-1\). Therefore, the equation of the line is \[ y = 4x - 1 \]

Final Answer The final answer is $\boxed{f(x) = 4x - 1}$