Question

Write an equation of the line passing through each of the following pairs of points.

Answer 1

Answer:

$y=\frac{1}{3}+\frac{13}{3}$

Step-by-step explanation:

We want to write the equation of a line that passes through (5, 6) and (-1, 4).

First, let's find our slope. We can use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's let (5, 6) be (x₁, y₁) and let's let (-1, 4) be (x₂, y₂). So, our slope is:

$m=\frac{4-6}{-1-5}$

Subtract:

$m=-2/-6$

Reduce:

$m=1/3$

So, our slope is 1/3.

Now, we can use the point-slope form, which is:

$y-y_1=m(x-x_1)$

For consistency, let's let (5, 6) be (x₁, y₁). We will also substitute 1/3 for m. So:

$y-6=\frac{1}{3}(x-5)$

Distribute:

$y-6=\frac{1}{3}x-\frac{5}{3}$

Add 6 to both sides:

$y=\frac{1}{3}x-\frac{5}{3}+\frac{18}{3}$

Add:

$y=\frac{1}{3}+\frac{13}{3}$

And we're done!