WHOEVER EXPLAINS ALL THEIR WORK AND GOES THROW EAXH STEP WILL GET BRAINLEST THAT IS COMPLETELY FINISEHD. write the equation of the line that goes through the points (3,2) (4,-1) show ALL steps and EXPLAIN what you are doing in each step. you will be graded on showing all the steps and your explanation.

Step-by-step explanation:

I accept your challenge!

First we know that a equation of the line is a linear equation, and its equation is:

In this context, the slope, defined as the steepness of a line is characterized as the ratio of RISE (the difference in the y-coordinates, the vertical change) over the RUN (the difference in x-coordinates, the horizontal change).

Once we know two points where the line goes through, we can get the slope, once we know the change in y and x.

I will take as Point 1 and as Point 2.

So,

Now we have to find the y-intercept:

To do so, think about the the points given and the nearly finished equation, we can find b with those two informations.

Our currently equation of the line is:

Using the points, take Point 1 as an example, it says that when , so plugging it in the equation:

Taking the Point 2

Now we found ! The equation is complete!