Questions: Determine if the given equation represents a linear relationship: Determine whether the equation y/9=x is linear. Find the slope of any nonvertical line.

Determine if the given equation represents a linear relationship: Determine whether the equation y/9=x is linear. Find the slope of any nonvertical line.

Transcript text: Determine if the given equation represents a linear relationship: Determine whether the equation $\frac{y}{9}=x$ is linear. Find the slope of any nonvertical li

Solution

Solution Steps

To determine if the given equation represents a linear relationship, we need to check if it can be written in the form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. If it can, then it is a linear equation. We will also find the slope $ m $.

Step 1: Rewrite the Given Equation

The given equation is: \[ \frac{y}{9} = x \]

Step 2: Solve for $ y $

To determine if the equation is linear, we need to solve for $ y $: \[ y = 9x \]

Step 3: Check if the Equation is Linear

An equation is linear if it can be written in the form $ y = mx + b $. The equation $ y = 9x $ is in this form with $ m = 9 $ and $ b = 0 $. Therefore, the equation is linear.

Step 4: Determine the Slope

The slope $ m $ of the equation $ y = 9x $ is: \[ m = 9 \]