Question

Which equation represents the line that passes through (-6, 7) and (-3, 6)

Answer 1

Answer:

x + 3y - 16 = 0

Step-by-step explanation:

When two points, say $(x_1, y_1)$ and $(x_2, y_2)$ are given, the equation is determined using Two - point form.

The two - point form is as follows:

$\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$

Here: $(x_1, y_1) = (-6, 7)$ and $(x_2, y_2) = (-3, 6)$.

Substituting in the formula we get the equation of the line as:

$\frac{y - 7}{6 - 7} = \frac{x + 6}{- 3 + 6}$

$\implies \frac{y - 7}{- 1} = \frac{x + 6}{ 3}$

$\implies 3y - 21 = - x - 6$

Rearranging we get: x + 3y - 15 = 0

This is the required equation of the line.