Answer:

Step-by-step explanation:
We are given that a line contains the points (4, -2) and (6, 1)
We want to write the equation of the line that contains these points
There are a couple of ways to write the equation of the line, but the most common way is slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y-intercept
First, we need to find the slope of the line
The slope (m) can be calculated using the formula
, where
and
are points
Let's first label the values of the points to avoid any confusion and mistakes before calculating:

Now substitute into the formula
m=
m=
m=
Simplify
m=
The slope is 3/2
We can substitute this as m in our line.
Here is our line so far:
y = 3/2x + b
Now we need to solve for b
As the line passes through both (4, -2) and (6, 1), we can use either one of them to help solve for b.
Taking (4, -2) for example:
-2 = 3/2(4) + b
Multiply
-2 = 6 + b
Subtract 6 from both sides
-8 = b
Substitute into the equation
y = 3/2x - 8
Topic: finding the equation of the line
See more: brainly.com/question/27726732