Questions: Find a formula for the linear function depicted in the following graph.

Transcript text: Find a formula for the linear function depicted in the following graph.

Solution

Solution Steps

Step 1: Identify two points on the line

From the graph, we can identify two points on the line. Let's choose the points \((-5, -5)\) and \((5, 5)\).

Step 2: Calculate the slope (m)

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \((-5, -5)\) and \((5, 5)\): \[ m = \frac{5 - (-5)}{5 - (-5)} = \frac{10}{10} = 1 \]

Step 3: Use the slope-intercept form to find the y-intercept (b)

The slope-intercept form of a line is: \[ y = mx + b \] Using one of the points \((-5, -5)\) and the slope \(m = 1\): \[ -5 = 1(-5) + b \] \[ -5 = -5 + b \] \[ b = 0 \]