Let's begin by identifying key information given to us:
The general equation of a straight line is represented by the equation:
[tex]\begin{gathered} y=mx+b \\ where\colon m=slope,b=x-intercept \end{gathered}[/tex]The equation has a slope of -3. Hence, the equation becomes:
[tex]\begin{gathered} y=mx+b \\ m=-3 \\ \Rightarrow y=-3x+b \end{gathered}[/tex]We were given that equation passed through the point (1, 9)
Since we were given one point, we will use the point-slope equation to obtain the equation of this straight line. We have it thus:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(1,9) \\ y-9=-3(x-1) \\ y-9=-3x+3 \\ \text{Add ''9'' to both sides, we have:} \\ y-9+9=-3x+3+9 \\ y=-3x+12 \end{gathered}[/tex]Therefore, the equation of the straight line is: y = -3x + 12
