Step-by-step explanation:
Given the two linear equations with two variables:
[tex]\displaystyle\mathsf{\Bigg\{\left{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!Equation(1):\:y\:=\:\frac{1}{6}x+5\:\Rightarrow slope(m)=\frac{1}{6},\:y-intercept:\:(0,\:5)} \atop {\!\!\!Equation(2):\:y\:=\:-\frac{3}{2}x-5}\:\Rightarrow slope(m)=-\frac{3}{2},\:y-intercept:\:(0,\:-5)} \right. }[/tex]
Start by plotting the y-intercepts of each equation on the graph.
Equation 1: y-intercept: (0, 5)
Equation 2: y-intercept: (0, -5)
Next, using the slope of each equation, use the "Rise over run" technique to plot other points on the graph. In other words:
Equation 1: slope = ⅙ ⇒ Rise 1 unit, run 6 units to the right.
[tex]\displaystyle\mathsf{Equation\:2:\:slope(m)\:=-\frac{3}{2}\:\Rightarrow\:\:Down\:3\: units, run\:2\:units\:to\:the\:right. }[/tex]
Attached is the screenshot of the graphed linear equations using the techniques discussed in this post.
