Question

What point slope form equation could be produced with the points(-3,-6)and (3,-3)

Answer 1

y+6=1/2(x+3)

Explanation:

Hi there!

We want to find the equation of the line in point-slope form that passes through (-3, -6), and (3, -3)

Point-slope form is given as y-
`y_(1)`=m(x-
`x_(1)`) where (
`x_(1)`,
`y_(1)`) is a point and m is the slope

We don't know the slope of the line, so let's find it

The formula for the slope (m) calculated from two points is
`(y_(2)-y_(1))/(x_(2)-x_(1))`, where (
`x_(1)`,
`y_(1)`) and (
`x_(2)`,
`y_(2)`) are points

We have two points, but let's label their values to avoid any confusion

`x_(1)`=-3

`y_(1)`=-6

`x_(2)`=3

`y_(2)`=-3

Now substitute into the formula (remember: the formula has SUBTRACTION)

m=
`(-3--6)/(3--3)`

simplify

m=
`(-3+6)/(3+3)`

m=
`(3)/(6)`

m=1/2

So the slope of the line is 1/2

Now that we have everything needed for point-slope form (a point and the slope), substitute the values into the formula (remember: the formula has SUBTRACTION)

y-
`y_(1)`=m(x-
`x_(1)`)

y--6=1/2(x--3)

simplify

y+6=1/2(x+3)

Hope this helps!