Question

slope intercept form
write the equation for the line.
$y = mx + b$
(there is a coordinate plane with a line, and a formula $y = \square x + \square$ to fill in)

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. Let's take (0, -1) and (3, 0). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the values: \( m = \frac{0 - (-1)}{3 - 0} = \frac{1}{3} \).

Step3: Write the equation

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

Answer:

\( y = \frac{1}{3}x - 1 \) (So the first box is \( \frac{1}{3} \) and the second box is -1)