Answer
Slope: $m=\dfrac{1}{2}$
$x$-intercept $=$ $y$-intercept $=$ $(0,0)$
Work Step by Step
$y-3=\dfrac{1}{2}(x-6)$
Express this equation in slope-intercept form by solving it for $y$:
$y-3=\dfrac{1}{2}x-\dfrac{6}{2}$
$y-3=\dfrac{1}{2}x-3$
$y=\dfrac{1}{2}x-3+3$
$y=\dfrac{1}{2}x$
This line is now in slope-intercept form, which is $y=-mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept.
Comparing the given line to the slope-intercept form, it can be seen that $m=\dfrac{1}{2}$ and $b=0$
The slope of the given line is $m=\dfrac{1}{2}$ and its $y$-intercept is the origin, $(0,0)$
Since the $y$-intercept is the origin, then the $x$-intercept of this line is also the point $(0,0)$
