Question

In two or more complete sentences describe the process in writing the equation of a line given two points? there are no points I just need to know the process of writing the equation if there were points. need answer ASAP

Answer 1

Given the two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$, we are going to use the slope formula, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$, to find the slope of the line passing throughout our two points; then, we are going to replace the values in the point slope formula, $y=m(x-x_{1})+y_{1}$, and simplify to complete the equation of our line.

Let's check this out with an example:

suppose you have the points (1,5) and (3,8), so $x_{1}=1$, $y_{1}=5$, $x_{2}=3$, and $y_{2}=8$.

First, we are going to use the slope formula to find the slope of the line passing throughout our two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{8-5}{3-1}$

$m=\frac{3}{2}$

Now that we have the slope of our line, we can use the point slope formula to complete our line equation:

$y=m(x-x_{1})+y_{1}$

$y=\frac{3}{2}(x-1)+5$

$y=\frac{3}{2} x-\frac{3}{2} +5$

$y=\frac{3}{2} x+\frac{7}{2}$

Answer 2

First u would use the slope formula : (y2 - y1) / (x2 - x1) to find the slope.
You would then use y = mx + b formula......sub in ur slope for m...and u would sub in one set of ur points (x,y), it does not matter which set of points u use.
You would then solve for b, ur y int.

Example : (1,2)(3,4)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (4 - 2) / (3 - 1) = 2/1 or just 2

y = mx + b
slope(m) = 2
use either of ur points (1,2)...x = 1 and y = 2
now sub and find b
2 = 2(1) + b
2 = 2 + b
2 - 2 = b
0 = b

so ur equation is : y = 2x + 0....or just y = 2x