Question

What is an equation of the line that passes through the points (4, -2) and (6, 1)?

Answer 1

Answer:

$y=\frac{3}{2}x - 8$

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 $\frac{y_2- y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

Let's first label the values of the points to avoid any confusion and mistakes before calculating:

$x_1 =4\\y_1=-2\\x_2=6\\y_2=1$

Now substitute into the formula

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

m=$\frac{1--2}{6-4}$

m=$\frac{1+2}{6-4}$

Simplify

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

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: https://brainly.com/question/27726732