The equation of line through given points is:
[tex]y=\frac{4}{3}x+\frac{10}{3}[/tex]
Step-by-step explanation:
Given
(x1,y1) = (2,6)
(x2,y2) = (-4,-2)
Slope-intercept form is:
[tex]y=mx+b[/tex]
We have to find the slope first
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Putting\ values\\m=\frac{-2-6}{-4-2}\\=\frac{-8}{-6}\\=\frac{4}{3}[/tex]
Putting the value of slope in the equation
[tex]y=\frac{4}{3}x+b[/tex]
To get the value of b, we will put (2,6) in the equation
[tex]6=\frac{4}{3}(2}+b\\6=\frac{8}{3}+b\\b=6-\frac{8}{3}\\b=\frac{18-8}{3}\\b=\frac{10}{3}[/tex]
Putting the values of b and m we get
[tex]y=\frac{4}{3}x+\frac{10}{3}[/tex]
The equation of line through given points is:
[tex]y=\frac{4}{3}x+\frac{10}{3}[/tex]
Keywords: Equation of line, Slope
Learn more about equation of line at:
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