Answer:
[tex]y=\frac{-2}{3}x+8[/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 (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the given points [tex](x_1,y_1)[/tex] are [tex](x_2,y_2)[/tex]
Plug in the given points (0,8) and (3,6)
[tex]m=\frac{6-8}{3-0}\\m=\frac{-2}{3}[/tex]
Therefore the slope of the line is [tex]\frac{-2}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{-2}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{-2}{3}x+b[/tex]
The y-intercept occurs when x=0. One of the given points is (0,8), so therefore, the y-intercept is 8. Plug this into [tex]y=\frac{-2}{3}x+b[/tex]:
[tex]y=\frac{-2}{3}x+8[/tex]
I hope this helps!
