Solution:
To graph the equation x + 4y = 8, follow these steps:
[tex]\noindent\rule{12cm}{0.4pt}[/tex]
1. Rewrite the Equation in Slope-Intercept form:
[tex]\text{The slope-intercept form of a line is $y=mx+b,$ where $m$ is the slope and $b$}\\\text{is the $y$-intercept.}[/tex]
[tex]x+4y=8\\4y=-x+8\\\\y=-\dfrac{1}{4}x+2[/tex]
[tex]\text{Now, the equation is in the form $y=mx+b$, where $m=-\dfrac{1}{4}$ and $b=2.$}[/tex]
[tex]\noindent\rule{12cm}{0.4pt}[/tex]
2. Identify the y-intercept.
[tex]\text{The $y$-intercept is the value of $y$ when $x=0.$}\\\\\text{From the equation $y=-\dfrac{1}{4}x+2,$ when $x=0:$}\\\text{$y=2$}\\\\\text{So, the $y$-intercept is (0,2).}[/tex]
[tex]\noindent\rule{12cm}{0.4pt}[/tex]
3. Identify the x-intercept.
[tex]\text{The $x$-intercept is the value of $x$ when $y=0.$}\\\\\text{From the original equation $x+4y=8,$ when $y=0:$}\\x+4(0)=8\\x=8\\\\\text{So, the $x$-intercept is (8,0).}[/tex]
[tex]\noindent\rule{12cm}{0.4pt}[/tex]
4. Plot the intercepts:
- Plot the y-intercept (0,2).
- Plot the x-intercept (8,0).
[tex]\noindent\rule{12cm}{0.4pt}[/tex]
5. Join the plotted points.
- Connect the two points (0,2) and (8,0) with a straight line.
