Question

Which equation represents the line that passes through the points (-3 7) and (9 -1)

Answer 1

Given the points:

(x1, y1) ==> (-3, 7)

(x2, y2) ==> (9, -1)

The equation is of the form: y = mx + b

Where m is the slope and b is the y-intercept.

Let's find the slope:

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ \\ m=(-1-7)/(9-(-3)) \\ \\ m\text{ = }(-8)/(12) \\ \\ m=-(2)/(3) \end{gathered}`

We have:

`y=-(2)/(3)x+b`

To find b, input any of the given points for x and y

`\begin{gathered} 7=-(2)/(3)(-3)+b \\ \\ 7=2\text{ + b} \\ \\ 7-2=b \\ \\ 5=b \end{gathered}`

Therefore, the equation that represents the line is:

`y=-(2)/(3)x+5`

ANSWER:

`y=-(2)/(3)x+5`