The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Equation of a line
From the question, we are to determine the equation of the line that passes through the given points
Using the formula
[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the give information,
[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]
[tex]y_{2} = 6\\[/tex]
Putting the parameters into the formula,
[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]
[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]
∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Learn more on Equation of a line here: https://brainly.com/question/12079926
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