Answer
Slope: $m=-\dfrac{4}{9}$
$x$-intercept: $\Big(\dfrac{3}{4},0\Big)$
$y$-intercept: $\Big(0,\dfrac{1}{3}\Big)$
Work Step by Step
$4x+9y=3$
Express this equation inslope-intercept form by solving it for $y$:
$9y=-4x+3$
$y=-\dfrac{4}{9}x+\dfrac{3}{9}$
$y=-\dfrac{4}{9}x+\dfrac{1}{3}$
This line is now in slope-intercept from, 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 $m=-\dfrac{4}{9}$ and $b=\dfrac{1}{3}$
The slope of the given line is $m=-\dfrac{4}{9}$ and its $y$-intercept is the point $\Big(0,\dfrac{1}{3}\Big)$
To find the $x$-intercept, set $y$ equal to $0$ in the original equation and solve for $x$:
$4x+9(0)=3$
$4x=3$
$x=\dfrac{3}{4}$
The $x$-intercept of the given line is the point $\Big(\dfrac{3}{4},0\Big)$
