Questions: For the graph of the linear function f(x)=mx+b, m is the and b is

Transcript text: For the graph of the linear function $f(x)=m x+b, m$ is the $\qquad$ and $b$ is $\qquad$

Solution

Solution Steps

To determine the roles of $ m $ and $ b $ in the linear function $ f(x) = mx + b $:

$ m $ represents the slope of the line, which indicates the rate of change of $ y $ with respect to $ x $.
$ b $ represents the y-intercept, which is the point where the line crosses the y-axis.

Step 1: Identify the Slope and Y-Intercept

Given the linear function $ f(x) = mx + b $, we need to identify the values of $ m $ and $ b $.

From the output:

$ m = 2 $
$ b = 3 $

Step 2: Interpret the Slope

The slope $ m $ represents the rate of change of $ y $ with respect to $ x $. In this case, $ m = 2 $, which means that for every unit increase in $ x $, $ y $ increases by 2 units.

Step 3: Interpret the Y-Intercept

The y-intercept $ b $ is the point where the line crosses the y-axis. In this case, $ b = 3 $, which means that when $ x = 0 $, $ y = 3 $.