Question

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

Answer 1

7x + 4y = 17 is the equation of line passing through points (3, -1) and (-1, 6)

Solution:

Given that we have to find the equation of line passing through points (3, -1) and (-1, 6)

Let us first find the slope of line

The slope of line is given as:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Here in this sum,

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

Substituting the values in given formula we get,

`m = (6-(-1))/(-1-3)\\\\m = (6+1)/(-4)\\\\m = (-7)/(4)`

The equation of line in slope intercept form is:

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

Where "m" is the slope of line and "c" is the y - intercept

Find the y - intercept:

Substitute (x, y) = (3, -1) and
`m = (-7)/(4)` in eqn 1

`-1 = (-7)/(4)(3) + c\\\\-1 = (-21)/(4) + c\\\\-1 = (-21+4c)/(4)\\\\-4 = -21+4c\\\\4c = 17\\\\c = (17)/(4)`

Substitute
`m = (-7)/(4) \text{ and } c = (17)/(4)` in slope intercept form

`y = (-7)/(4)x + (17)/(4)`

Thus the equation of line in slope intercept form is found

Writing in standard form,

4y = -7x + 17

7x + 4y = 17

Thus the equation of line in standard form is also found