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:

$y = \frac{5}{3}x -4$

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

$m = \frac{y_2-y_1}{x_2-x_1}$

From given,

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

Substituting the values we get,

$m = \frac{6-1}{6-3}\\\\m = \frac{5}{3}$

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

$1 = \frac{5}{3} \times 3 + c\\\\1 = 5 + c\\\\c = -4$

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

$y = \frac{5}{3}x -4$

Thus the equation of line in slope intercept form is found