The equation that represents the line is:
[tex]y = \frac{5}{6}x+\frac{8}{3}[/tex]
Step-by-step explanation:
We have to observe the graph to find the points on line
So the points on line are:
(x1,y1) = (4,6)
(x2,y2) = (-2,1)
First of all we have to find the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{1-6}{-2-4}\\=\frac{-5}{-6}\\=\frac{5}{6}[/tex]
Equation of line is given by:
[tex]y=mx+b[/tex]
Putting the value of slope
[tex]y = \frac{5}{6}x +b[/tex]
Putting (4,6) in the equation
[tex]6 = \frac{5}{6}(4)+b\\6 = \frac{20}{6} +b\\b = 6 - \frac[20}{6}\\b = \frac{36-20}{6}\\b = \frac{16}{6}\\b = \frac{8}{3}[/tex]
Putting the value of b
[tex]y = \frac{5}{6}x+\frac{8}{3}[/tex]
Hence,
The equation that represents the line is:
[tex]y = \frac{5}{6}x+\frac{8}{3}[/tex]
Keywords: Equation of line, slope
Learn more about equation of line at:
- brainly.com/question/537230
- brainly.com/question/5345266
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