The equation of the line is [tex]\rm y = \dfrac{2}{3} x+5[/tex].
Given that,
A line passes through (3, 7) and (6, 9).
We have to determine,
Which equation best represents the line?
According to the question,
The standard form of the equation of line is,
[tex]\rm y = mx+c[/tex]
To determine the line following all the steps given below.
A line passes through (3, 7) and (6, 9).
Then,
The slope of the line is,
[tex]\rm Slope= \dfrac{y_2-y_1}{x_2-x_1}\\\\ Slope= \dfrac{9-7}{6-3}\\\\Slope = \dfrac{2}{3}[/tex]
The slope of the line is 2/3.
Then,
The value of c is,
[tex]\rm y = mx+c\\\\7= \dfrac{2}{3}\times 3 +c\\\\c = 7-2\\\\c=5[/tex]
Therefore,
The equation of the line is,
[tex]\rm y = mx+c\\\\y = \dfrac{2}{3} x+5[/tex]
Hence, The equation of the line is [tex]\rm y = \dfrac{2}{3} x+5[/tex].
For more details refer to the link given below.
https://brainly.com/question/12895249
