Question

What is an equation of the line that passes through the points (-3, 8) and (6, 2)?

Answer 1

Answer:

y= -2/3x + 6

Step-by-step explanation:

Hi there!

We are given the points (-3, 8) and (6, 2)
We want to find the equation of the line that passes through these two points

There are 3 ways to write the equation of the line, with the most common way to write it being slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

So let's fine the slope of the line

The slope (m) of the line can be found with the formula $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have two points, which we need to find slope, but let's label their values to avoid confusion.

$x_1=-3\\y_1=8\\x_2=6\\y_2=2$

Now substitute these values into the formula

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

m=$\frac{2-8}{6--3}$

Simplify

m=$\frac{2-8}{6+3}$

m=$\frac{-6}{9}$

Simplify once again

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

The slope of the line is -2/3

Here's the equation of the line so far:
y=-2/3x+b

Now we need to find b

As the equation passes through the points  (-3, 8) and (6, 2), we can use either one of them to help find b

Using (-3, 8) for example:

8= -2/3(-3)+b

Multiply

8=2 + b

Subtract 2 from both sides

6 = b

Substitute 6 as b:

y= -2/3x + 6

Hope this helps!

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