Question

What is the equation of the line that passes through (4,-1) and (-2,3)

Answer 1

Answer:

2x+3y-5=0

Step-by-step explanation:

We have been given two points  (4,-1) and (-2,3). Now we need to find about

what is the equation of the line that passes through (4,-1) and (-2,3).

Slope of the line through the points  (4,-1) and (-2,3)  is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{3-\left(-1\right)}{-2-4}=\frac{3+1}{-6}=\frac{4}{-6}=-\frac{2}{3}$

Now plug the slope $m=-\frac{2}{3}$ and point (4,-1) into point slope formula

$y-y_1=m\left(x-x_1\right)$

$y--1=-\frac{2}{3}\left(x-4\right)$

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

or we can rewrite that as 2x+3y-5=0

Hence final answer is 2x+3y-5=0

Answer 2

Hello!

The answer is:

The second option

$2x+3y-5=0$

Why?

To know which is the equation of the line, we need to follow the next steps:

Find the slope of the line:

We are given the points:

$(-2,3)\\(4,1)$

Where,

$x_1=4\\y_1=-1\\x_2=-2\\y_2=3$

Also, we know that we can calculate the slope of a function using the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Now, using the slope formula, and substituting the given points, we have:

$m=\frac{3-(-1)}{-2-4}$

$m=\frac{4}{-6}$

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

Find the "b" value:

In order to find "b" we need to substitute any of the given points, we know that line pass through both of the given points, so, substituting the point (4,-1), we have:

Writing the slope form of the function,

$y=mx+b$

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

$-1=-\frac{2}{3}*(4)+b\\\\b=-1+\frac{2}{3}*(4)=-1+\frac{8}{3}=\frac{-3+8}{3}=\frac{5}{3}$

Now that we know the slope and "b", we can write the equation of the line in slope-intercept form:

Writing the equation of the equation, we have:

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

Then, by multiplying each side of the equation by 3 in order to simplify the fractions, we have:

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

$3y=-2x+5$

Rewriting the equation, we have:

$2x+3y-5=0$

Hence, we have that the correct option is the second option, the equation of the line that passes through the given points is:

$2x+3y-5=0$

Have a nice day!