Indicate in standard form the equation of the line passing through the given points.

E(-2,2)F(5,1)

Question

Indicate in standard form the equation of the line passing through the given points.

E(-2,2)F(5,1)

lgbasallote · Answer

hint: use the two point formula $$\large y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x-x_1)$$
does that help?

anonymous · Answer

ive tried it multiple times and i cant seem to understand it

hero · Answer

This is my first time seeing the two point formula.

anonymous · Answer

You are given two points. You probably know that for every two points in Euclidian space, there is a line that passes through them. The two-point formula given by lgbasallote is pretty useful, since you simply have to replace the coordinates of your points. I like to do it in steps, rephrasing the equation like this:

$$y-y_{0}=m(x-x_{0})$$

Where m is the slope of the line. There is a simple mnemonic technique to remember it:

$$m=\frac{ y_{2}-y_{1} }{x_{2}-x_{1}}=\frac{rise }{ run }$$

Now, what are these x0, x1, x2, y0, y1, y2? Simple. x0 and y0 are the coordinates a any point on the line (note that you were given two). And x1,x2, y1,y2 are the coordinates of any two points on the same line.

anonymous · Answer

Now, you simply replace. Let's start with the slope. You have to remember which coordinates are your 1 coordinates and which are your 2. It doesn't matter which point you choose as 1 or 2. So
$$m = \frac{ 2-1 }{ -2-5 }=\frac{ 1 }{ -7 }=-\frac{ 1 }{ 7 }$$

Now your two point equation becomes

$$y-y_{0}=-\frac{ 1 }{ 7 }(x-x_{0})$$

And you now choose any of the two points you were given and replace their coordinates in y0 and x0. Afterwards, you generally want to solve for y.

$$y-1=-\frac{ 1 }{ 7 }(x-5)$$

$$y=-\frac{ x }{ 7 } +\frac{ 5 }{ 7 } +1$$

$$y=\frac{12 }{ 7 }- \frac{ x }{ 7 } $$