Answer
The graph of the lines is shown below:
Work Step by Step
Point $(3,4)$
$a)$ $m=1$
Using the point-slope form of the equation of a line, the equation of this line is:
$y-y_{0}=m(x-x_{0})$
$y-4=(1)(x-3)$
$y-4=x-3$
$y=x-3+4$
$y=x+1$
$b)$ $m=-2$
Using the point-slope form of the equation of a line, the equation of this line is:
$y-y_{0}=m(x-x_{0})$
$y-4=(-2)(x-3)$
$y-4=-2x+6$
$y=-2x+6+4$
$y=-2x+10$
$c)$ $m=-\dfrac{3}{2}$
$y-y_{0}=m(x-x_{0})$
$y-4=-\dfrac{3}{2}(x-3)$
$y-4=-\dfrac{3}{2}x+\dfrac{9}{2}$
$y=-\dfrac{3}{2}x+\dfrac{9}{2}+4$
$y=-\dfrac{3}{2}x+\dfrac{17}{2}$
$d)$ Slope undefined
If the slope is undefined, the line is a vertical line with $x$-coordinate equal to $3$
The equation of the line is:
$x=3$
