Question

what is the function rule for the linear function in this graph?
slope–intercept form
y = mx + b
graph of a line with points at (-3, 0) and (0, 2) and (3, 4)
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, 2), so \( b = 2 \).

Step2: Calculate the slope (m)

We can use two points on the line, e.g., (-3, 0) and (0, 2). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points: \( m=\frac{2 - 0}{0 - (-3)}=\frac{2}{3} \).

Step3: Write the function rule

Using the slope - intercept form \( y = mx + b \), substitute \( m=\frac{2}{3} \) and \( b = 2 \). So the function rule is \( y=\frac{2}{3}x + 2 \).

Answer:

\( y=\frac{2}{3}x + 2 \) (The numerator of the slope is 2, the denominator is 3, and the y - intercept is 2)