Question

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

Answer 1

Answer:

y = -(2/3)x + 5/3

Step-by-step explanation:

Label the points that are given.  

(4, -1) = (x1, y1)

(-2, 3) = (x2, y2)

Step 1: Find the slope, denoted m

This is done by using the formula m = (y2 - y1)/(x2 - x1)

The slope for this problem is

m = (3 - (-1))/(-2 - 4)  

m = 4/-6 = -2/3

Step 2: The general form for a linear equation in slope-intercept form is  

y = mx + b where m is the slope and b is the y-intercept

Use what we know about our line to solve the rest. By using one of the given points, we have 3 of the 4 variables in the above equation. Pick either point, it doesn't matter which one. We'll use (4, -1), which is (x, y), and we know that  

m = -2 /3

The equation becomes...

-1 = -(2/3)(4) + b (now solve for b)

-1 =  -8/3 + b

-1 + 8/3 = b

-3/3 + 8/3 = b

5/3 = b

Plug that value into the general form...

y = -(2/3)x + 5/3

Answer 2

Answer:

2x + 3y =  5.

Step-by-step explanation:

First find the slope  of the line:

Slope = (3 - (-1)) / (-2-4)

= 4/-6 = -2/3

Now we use the point slope form of a straight line:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

y - 3 = -2/3(x - (-2))

y - 3 = -2/3(x + 2)

3y - 9 = -2x - 4

2x + 3y = 5.