Question

what is the equation of a line that passes through (1,3) and (4,9)

Answer 1

y = 2x + 1 is the equation of a line that passes through (1,3) and (4,9)

Solution:

Given that we have to write the equation of a line that passes through (1,3) and (4,9)

Let us first find the slope of line

The slope of line is given as:

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

Here the given points are (1,3) and (4,9)

$(x_1, y_1) = (1, 3)\\\\(x_2, y_2) = (4, 9)$

Substituting the values in formula, we get,

$m = \frac{9-3}{4-1}\\\\m = \frac{6}{3} = 2$

Thus slope of line is 2

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope and "c" is the y - intercept

To find the y intercept, substitute (x, y) = (1, 3) and m = 2 in eqn 1

3 = 2(1) + c

c = 1

Thus the equation of line is:

Substitute c = 1 and m = 2 in eqn 1

y = 2x + 1

Thus equation of line is found