A linear equation the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
To find "m" and "b", follow the steps below.
Step 01: Substitute the slope in the equation.
According to the problem, the slope is -2. That is, m = -2.
Then,
[tex]y=-2x+b[/tex]Step 02: Substitute the point (-4, 9) in the equation.
(-4, 9) means x = -4 and y = 9. Then,
[tex]\begin{gathered} 9=-2\cdot(-4)+b \\ 9=8+b \end{gathered}[/tex]Subtract 8 from both sides to find b.
[tex]\begin{gathered} 9-8=8+b-8 \\ 1=0+b \\ 1=b \end{gathered}[/tex]Substituting "m" and "b" in the equation:
[tex]y=-2x+1[/tex]Answer:
[tex]y=-2x+1[/tex]