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 value of y when x = 0. From the graph, when x = 0, y = 1. So, \( b = 1 \).

Step2: Calculate the slope (m)

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

Step3: Write the function rule

Using the slope-intercept form \( y = mx + b \), substitute m = 3 and b = 1. So the function rule is \( y = 3x + 1 \).

Answer:

\( y = 3x + 1 \)