Answer:
[tex]y=\displaystyle -\frac{5}{3}x+7[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept
We're given that the slope is [tex]\displaystyle -\frac{5}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle -\frac{5}{3}x+b[/tex]
Now, to solve for the y-intercept, plug in the point (3,2) and solve for b:
[tex]2=\displaystyle -\frac{5}{3}(3)+b\\\\2=-5+b\\b=7[/tex]
Therefore, the y-intercept of the line is 7. Plug this back into [tex]y=\displaystyle -\frac{5}{3}x+b[/tex]:
[tex]y=\displaystyle -\frac{5}{3}x+7[/tex]
I hope this helps!
