Answer
please see image
Work Step by Step
Graphically,
$m$ is the slope of the line $y=mx+b$:
$m=\displaystyle \frac{\Delta y}{\Delta x} =\displaystyle \frac{Rise}{Run}$
b is the y-intercept
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First, write the equation in the form $y=mx+b$
$2x-3y=1\qquad/-2x$
$-3y=-2x+1\qquad/\div(-3)$
$y=\displaystyle \frac{2}{3}x-\frac{1}{3}$
from where we read:
slope=$\displaystyle \frac{2}{3}$,
y-intercept: $-\displaystyle \frac{1}{3}$.
1. Determine the y-intercept, and plot the point $(0,-\displaystyle \frac{1}{3})$
2. Use the run-rise logic:
for an increase in x by $3$,
y will change by $+2$.
Moving to the right by three units from $(0,-\displaystyle \frac{1}{3})$,
the point we arrive at is $(0+3,-\displaystyle \frac{1}{3}+\frac{6}{3})=(3, \frac{5}{3}).$
Plot the second point.
Two points define a line.
Draw a straight line through these two points.
