Answer:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (15,2.2) and (5,1.6):
[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]
Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]
Plug in a given point and solve for b:
[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]
Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]
I hope this helps!
