Question

I need help on one more problem and thank you. I partially understand how to do this just a little more explaining could help.

Answer 1

So,

To find the equation of the line given, we are going to follow the steps:

1. Identify two points that lie on the line.

As you can see, we could take the points (3 , -4) and (6 , -2).

2. Find the slope between both points. The slope is just the divition of the change of y-units between the points and the change of x-units between the points.

This, is:

3. We could use the main equation of a line:

`y=mx+b`

Where m is the slope and (x,y) is a point that lie on the line.

What we're going to do, is to replace a point (x,y) and the slope that we just found so we can find the value of b and replace these values to find the equation.

So, let's replace (x,y) = (6,-2) and m=2/3:

`\begin{gathered} y=mx+b \\ -2=(2)/(3)(6)+b \\ -2=4+b \\ b=-6 \end{gathered}`

Now, replace m and b in the equation for slope-intercept form:

`y=mx+b\to y=(2)/(3)x-6`