Mathematics: 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.

Thank you so much. Have a nice day!...

WHOEVER EXPLAINS ALL THEIR WORK AND GOES THROW

Ответ:

labrandonanderson00

28.01.2022

Mathematics

y = -3x+11

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:

y = mx+b

$m: \text{slope}\\b: \text{y-intercept}$

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).

$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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 (3,2) as Point 1 and (4,-1) as Point 2.

So, $x_{1}=3 \text{ and } y_{1}=2\\x_{2}=4 \text{ and } y_{2}=-1$

$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{-1-2}{4-3}$

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

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:

y = -3x+b

Using the points, take Point 1 as an example, it says that when x = 3, y = 2 , so plugging it in the equation:

$2 = -3(3)+b\\2 = -9+b\\11 = b$

Taking the Point 2

$-1 = -3(4)+b\\-1 = -12+b\\11 = b$

Now we found ! The equation is complete!

y = -3x+11

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