Question

sketch a graph of y = f(x).
f(x) = \frac{1}{4}x + 8

use the graphing tool to graph the line.
click to enlarge graph

Explanation:

Step1: Find the y - intercept

The equation is in the form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{1}{4}x + 8\), when \(x = 0\), \(y=8\). So one point is \((0,8)\).

Step2: Find another point using the slope

The slope \(m=\frac{1}{4}\). From the point \((0,8)\), using the slope formula \(\text{slope}=\frac{\Delta y}{\Delta x}\), if \(\Delta x = 4\), then \(\Delta y=1\). So another point is \((4,9)\) (since \(x = 0+4=4\) and \(y=8 + 1=9\)).

Step3: Plot the points and draw the line

Plot the points \((0,8)\) and \((4,9)\) on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points \((0,8)\) and \((4,9)\) and draw a straight line through them to graph \(y=\frac{1}{4}x + 8\).