[tex]y=-x-6[/tex]
1) We're going to tackle this question by examining the graph and picking two points from that line. Namely, (-5,-1) and (3,-9)
2) So let's plug them into the slope formula, so that we can find the slope, i.e. the measure of how steep is that line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-9-(-1)}{3-(-5)}=\frac{-9+1}{3+5}=\frac{-8}{8}=-1[/tex]
3) The next step is to find the y-intercept. We can see in the graph that the line intercepts the y-axis at y=-6. But let's test it by finding the linear coefficient "b" algebraically:
[tex]\begin{gathered} (-5,-1),\text{ m=-1} \\ y=mx+b \\ -1=-1(-5)+b \\ -1=5+b \\ -1-5=5-5+b \\ b=-6 \end{gathered}[/tex]
Finally, we can write out the equation of the line in the slope-intercept form:
[tex]y=-x-6[/tex]
