Question

18b. write a rule (equation) for the graph below. * graph of a line with y-intercept at 10, and a slope indicated by +4 for a run of +1

Explanation:

Step1: Identify the slope (m)

The slope \( m \) is calculated as the change in \( y \) over the change in \( x \). From the graph, the change in \( y \) is \( +4 \) and the change in \( x \) is \( +1 \), so \( m = \frac{4}{1} = 4 \).

Step2: Identify the y-intercept (b)

The line crosses the y-axis at \( y = 10 \), so the y-intercept \( b = 10 \).

Step3: Use the slope-intercept form

The slope - intercept form of a linear equation is \( y = mx + b \). Substituting \( m = 4 \) and \( b = 10 \) into the formula, we get \( y = 4x+10 \).

Answer:

\( y = 4x + 10 \)