Answer
(a)
slope = $\frac{-1}{3}$.
y-intercept: $(0, 2)$
x-intercept: $(6, 0)$
(b) $y=-\frac{1}{3}x+2$.
Work Step by Step
RECALL:
(1) The slope is the ratio rise (change in y) over run (change in x).
(2) The x-intercept is the point where the graph touches/crosses the x-axis.
(3) The y-intercept is the point where the graph touches/crosses the y-axis.
(4) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
(a) From the point $(0, 2)$ to the point $(3, 1)$, the change in $y$ is $-1$ while the change in $x$ is $3$. Thus, the slope is $\frac{-1}{3}$.
The graph crosses the y-axis at the y-intercept $(0, 2)$.
With a slope of $-\frac{1}{3}$, for a change of $3$ units in $x$, there corresponds a 1-unit decrease in the value of $y$. Thus, from $(3, 1)$, a 3-unit increase in $x$ gives a 1-unit decrease in $y$ leading to the x-intercept of $(6, 0)$
(b) With a slope of $-\frac{1}{3}$ and a y-intercept of $(0, 2)$, then the equation of the line is $y=-\frac{1}{3}x+2$.
