# What is the equation in point-slope form of the line that passes through equation in the given points (4,1) and (-2,7)?

Apr 13, 2018

$y - 1 = - \left(x - 7\right)$

Here's how I did it:

#### Explanation:

Point-slope form is shown here:

As you can see, we need to know the value of the slope and one point value.

To find the slope, we use the formula $\left(\text{change in y")/("change in x}\right)$, or $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

So let's plug in the value of the points:
$\frac{7 - 1}{- 2 - 4}$

Now simplify:
$\frac{6}{-} 6$

$- 1$

The slope is $- 1$.

Since we have the value of two points, let's put one of them into the equation:
$y - 1 = - \left(x - 7\right)$

Hope this helps!