Equation of a Line in Standard Form

In this problem, we need to find the equation of a line passing through two points, and we want the final answer in standard form.

First, let's find the slope of the line, often represented as m. The formula for slope is the change in y divided by the change in x.

Let's plug in our values. We'll use negative one minus five for the numerator, and twenty minus negative ten for the denominator.

This simplifies to negative six over thirty.

Dividing both numbers by six, we get a simplified slope of negative one fifth.

Now that we have the slope, we can use the point-slope formula to find the equation. Let's use the first point, negative ten and five.

Plugging in our values, we have y minus five equals negative one fifth times the quantity x minus negative ten.

Notice that x minus negative ten is the same as x plus ten.