# How do you write the equation for a line that passes through points (2,1) and (0,7)?

Dec 14, 2016

$y - 7 = - 3 x$ or $y = - 3 x + 7$

#### Explanation:

To find the equation of a line passing through two points you must first find the slope of the line.

The slope can be found by using the formula: color(red)(m = (y_2 = y_1)/(x_2 - x_1)
Where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points. Substituting the two points give in the problem allows us to calculate the slope as:

$m = \frac{7 - 1}{0 - 2}$

$m = \frac{6}{- 2}$

$m = - 3$

Next we can use the point-slope formula to find the equation for the line passing through these two points.

The point-slope formula states: $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
Where $m$ is the slope and #(x_1, y_1) is a point the line passes through.

We can substitute $- 3$ for me and (0, 7) for the point giving:

$y - 7 = - 3 \left(x - 0\right)$

$y - 7 = - 3 x - 3 \cdot 0$

$y - 7 = - 3 x$

Solving for the slope intercept form gives:

$y - 7 + 7 = - 3 x + 7$

$y - 0 = - 3 x + 7$

$y = - 3 x + 7$