Question

How do you graph `y-6=3(x-4)`?

Answer 1

By using slope intercept form and paper or a graphing calculator.

Explanation:

I'm going to detail two different methods. First graphing by hand and second by the calculator.

Both methods require us to get into slope intercept form so let's go ahead and do that. Slope intercept form is `y=mx+b` so from our equation all we need to do is distribute the three on the right side and add six to both sides.

`y-6=3(x-4)`
`y-6=3x-12`
`y=3x-6`

So the number added/subtracted at the end is our y-intercept. Since it's -6, our y intercept will be at `(0,-6)`. This can be proven by plugging x = 0 into the equation `y=3x-6`, you'll get `y=-6`.

So with that we have our starting point for the graph, so go ahead and make a graph on paper and put a dot at the point `(0,-6)`.

Now we can make additional dots by using our slope. The slope is 3 so for each time we go to the right one x coordinate, the line will go up 3. So on graph paper, you go over 1 square and up 3. Now continue going over and up until you have a line long enough to meet your personal standards.

Now if we want to graph it on the calculator, you just have to solve for y and plug in what y equals into your calculator. Or you can use an online service like desmos.com/calculator/ or something.

Below is what your final graph should look like.

graph{y=3x-6 [-16.15, 15.9, -7.18, 8.84]}