Question

Find an equation for the line below.

Answer 1

To find the equation of a line, you need to use the formula
`m=(y-y_0)/(x-x_0)=(rise)/(run)` to find the slope first.

To find the respective points that we need to plug into this formula, we need to use the axes and their values.

We can see that the first point (point on the left) has a position of (-1, -1). For the second point, we see that it has a position of (5, 1).

** remember, whenever you find the position of a point, it's always (x, y). Now that we have our values, we can plug and chug!

`m=(y-y_0)/(x-x_0)\\m= (1-(-1))/(5-(-1)) \\m=(1+1)/(5+1) \\m=(2)/(6) \\m=(1)/(3)`

So your answer should be 1/3 for your slope.

Now you need to find your y intercept, or what y will equal if x = 0. We can find this by using the information we now have. Remember, the equation for a linear line is
`y=mx+b`. So now, we plug in any of the two points (it doesn't matter which pair!) and solve for b!

`y=mx+b\\-1=(1)/(3)(-1)+b\\ -1=-(1)/(3)+b\\-1+(1)/(3)=b\\b=-(2)/(3)`

Now we have b!

So now, we can fully finish the equation of this line. Your final answer should be: y = (1/3)x - 2/3 or
`y=(1)/(3)x-(2)/(3)`.

Hope this helps!