Question

Find the equation of a line containing the points (3,1) and (2,5). Write the equation

Answer 1

Answer:

$y=-4x+13$

Step-by-step explanation:

So we know two points of a line and we want to find the equation of the line.

First, let's use the two points to find the slope.

The slope formula is:

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

Let's let (3,1) be x₁ and y₁ and let's let (2,5) be x₂ and y₂.

Therefore:

$m=\frac{5-1}{2-3}$

Simplify:

$m=4/=1=-4$

So, our slope is -4.

Now, let's find our equation using the point-slope form. The point-slope form is:

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

Let's continue to use (3,1) as x₁ and y₁. Our m or slope is -4. Thus:

$y-1=-4(x-3)$

Distribute the right:

$y-1=-4x+12$

Add 1 to both sides:

$y=-4x+13$

And we're done!