Question

enter the correct answer in the box.
a system of linear equations is shown on the graph. the equation of one of the lines is
y = -\frac{1}{3}x + 4. what is the equation of the other line in the system?
graph
y = mx + b

Explanation:

Step1: Identify the y-intercept (b)

The other line crosses the y-axis at (0, -1), so \( b = -1 \).

Step2: Calculate the slope (m)

We can use two points on the line. Let's take (0, -1) and (1, 2) (from the graph). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the points: \( m = \frac{2 - (-1)}{1 - 0} = \frac{3}{1} = 3 \).

Step3: Write the equation

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

Answer:

\( y = 3x - 1 \)