Question

as you answer the questions below, note the connections between finding slope from a graph and algebraically
slope is the rate of change of a linear function. it describes the ratio of change in y-values to change in x-values between points on a line.

1. use the graph to find the equation of the line.

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, -2), so the y-intercept \( b = -2 \).

Step2: Calculate the slope

Choose two points, e.g., (0, -2) and (1, 1). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{1 - 0} = \frac{3}{1} = 3 \).

Step3: Write the equation

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

Answer:

The equation of the line is \( y = 3x - 2 \)