Answer
$a)$ $y=-3x+12$
$b)$ $3x+y-12=0$
$c)$
Work Step by Step
The line that has $x$-intercept $4$ and $y$-intercept $12$
$a)$
The slope-intercept form of the equation of a line is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept.
Since both intercepts of the line are given, use them to find the slope:
$x$-intercept point: $(4,0)$
$y$-intercept point: $(0,12)$
$m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{12-0}{0-4}=\dfrac{12}{-4}=-3$
Both the slope of the line and its $y$-intercept are now known. Substitute them into the slope-intercept form of the equation of a line formula:
$y=-3x+12$
$b)$
To represent the equation of this line in its general form, just take all the terms on the right side to the left:
$3x+y-12=0$
$c)$
