Answer:
[tex]y=-\frac{2}{3}x+\frac{19}{3}[/tex]
Step-by-step explanation:
Lines that are perpendicular to each other have opposite reciprocal slopes. So, in this case, the slope that is perpendicular to 3/2 would be -2/3. In order for the line with that slope to pass (-4,9), we would need to plug in the coordinate point and solve for the y-intercept:
[tex]y=mx+b[/tex]
[tex]y=-\frac{2}{3}x+b[/tex]
[tex]9=-\frac{2}{3}(-4)+b[/tex]
[tex]9=\frac{8}{3}+b[/tex]
[tex]\frac{19}{3}=b[/tex]
Therefore, the equation in slope-intercept form would be [tex]y=-\frac{2}{3}x+\frac{19}{3}[/tex]
