Answer :
The equation of the line that passes through the points (3,1) and (6,6) is:
[tex]y = \frac{5}{3}x -4[/tex]
Solution:
Given that,
We have to find the equation of the line that passes through the points (3,1) and (6,6)
Find the slope of line
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From given,
[tex](x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (6, 6)[/tex]
Substituting the values we get,
[tex]m = \frac{6-1}{6-3}\\\\m = \frac{5}{3}[/tex]
The slope intercept form of line is given as:
y = mx + c ------ eqn 1
Where,
m is the slope
c is the y intercept
Substitute m = 5/3 and (x, y) = (3, 1) in eqn 1
[tex]1 = \frac{5}{3} \times 3 + c\\\\1 = 5 + c\\\\c = -4[/tex]
Substitute m = 5/3 and c = -4 in eqn 1
[tex]y = \frac{5}{3}x -4[/tex]
Thus the equation of line in slope intercept form is found