A line includes the points (4,2) and (7,8) . What is the equation in slope intercept form

y = 2x - 6

Step-by-step explanation:

It's not the only way, but I like to use point-slope form. Point-slope form is:

y - y₁ = m(x - x₁), where y₁ is any given y coordinate, x₁ is any given x coordinate, and m is the slope. Let's figure out the coordinates first.

Any coordinate can be used and you'll get the same answer. I'll use (4, 2) for this example: y - 2 = m(x - 4).

Next let's find m, the slope. We do this by using rise/run. The slope in this case is 6/3 = 2/1 = 2. The slope is 2. So...

y - 2 = 2(x - 4)

Now, let's simplify by using the distributive property:

y - 2 = 2*x - 2*4

y - 2 = 2x - 8.

Lastly, let's take a look at slope-intercept form: y = mx + b. The y is isolated, so to isolate y in our current equation, simply add 2 to both sides.

Your final answer should be y = 2x - 6.

Hope this helped!

x = 3 ± √(5+y)