Question

What is an equation of the line that passes through the points (3,1) and (6,6)?

Answer 1

The equation of the line that passes through the points (3,1) and (6,6) is:

`y = (5)/(3)x -4`

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

`m = (y_2-y_1)/(x_2-x_1)`

From given,

`(x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (6, 6)`

Substituting the values we get,

`m = (6-1)/(6-3)\\\\m = (5)/(3)`

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

`1 = (5)/(3) * 3 + c\\\\1 = 5 + c\\\\c = -4`

Substitute m = 5/3 and c = -4 in eqn 1

`y = (5)/(3)x -4`

Thus the equation of line in slope intercept form is found