Question

Write the equation of a line that passes through the points (−3, 7) and (3, 3)

y=−2/3x+5

y=2/3x+1

y=−2/3x+9

y=2/3x+9

Answer 1

Explanation:

You can write an equation of a line conveniently by point-slope form. It's in the form of
`y -a = m(x -b)` where
`(b,a)` is the coordinates of a point that's on the line and
`m` is the slope of the line.

Now choose a point (It doesn't really matter which one) and plug that in the equation. I'll choose
`(-3,7)` where
`a = 7` and
`b = -3`

`y -a = m(x -b) \\ y -7 = m(x -(-3)) \\ y -7 = m(x +3)`

The next thing we have to do now is finding the slope,
`m`, where it's equal to
`(y_(2) -y_(1))/(x_(2) -x_(1))\\`. I'll make
`(-3,7)` point 1 and
`(3,3)` point 2.

`m = (3 - 7)/(3 -(-3)) \\ m = (3 - 7)/(3 +3) \\ m = (-4)/(6) \\ m = -(2)/(3)`

Now let's plug that to our equation.

`y -7 = m(x +3) \\ y -7 = -(2)/(3)(x +3)`

Now we have the equation but out of all the choices it seemed that all of them are in slope-intercept form all you have to do now is make our equation rewrite it in slope-intercept form.

`y -7 = -(2)/(3)(x +3)\\ y -7 = -(2)/(3)x -(2)/(3)(3) \\ y - 7 = -(2)/(3)x -2\\ y = -(2)/(3)x +5`

Answer:

`y = -(2)/(3)x +5\\` is your equation.