Question

what is the function rule for the linear function in this graph? slope-intercept form y = mx + b y = ?x +

Explanation:

Step1: Find the y-intercept (b)

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at (0, 3), so \( b = 3 \).

Step2: Calculate the slope (m)

We can use two points on the line, for example, (0, 3) and (-1, -1). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the points: \( m=\frac{-1 - 3}{-1 - 0}=\frac{-4}{-1} = 4 \).

Answer:

\( y = 4x + 3 \)