Check the picture below.
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\qquad \underset{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}}\implies \cfrac{-2+4}{-2}\implies \cfrac{2}{-2}\implies -1[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y+4=-x+2\implies y=-x-2[/tex]
Answer:
[tex]y=-1x-2[/tex]
Step-by-step explanation:
Equation of a line is [tex]y=mx+b[/tex]
where m is the slope and b is the y intercept
Through the point (2,−4) with y-intercept of −2.
Y intercept is -2, the value of b is -2
(2,−4) is (x1.y1) and b=-2
plug in the value in y=mx+b
[tex]-4=m(2)-2[/tex], solve for m
add 2 on both sides
[tex]-2=m(2)[/tex]
divide 2 on both sides
m=-1
Equation of the line is
[tex]y=-1x-2[/tex]
Graph the equation using point (2,-4) and y intercept (0,-2)
the graph is attached below
