The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 8) and (1, 3).
Substitute:
[tex]m=\dfrac{3-8}{1-3}=\dfrac{-5}{-2}=2.5[/tex]
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The point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-8=2.5(x-3)[/tex]
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The slope-intercept form:
[tex]y=mx+b[/tex]
Substitute the value of a slope:
[tex]y=2.5x+b[/tex]
Substitute the coordinates of the point (1, 3) to the equation of line:
[tex]3=2.5(1)+b\\3=2.5+b\qquad|-2.5\\b=0.5[/tex]
Final, we have:
[tex]y=2.5x+0.5[/tex]
