Question

Find the equation for the line that passes through the points ( 7 , 2 ) and ( 10 , − 6 ) . Give your answer in slope intercept form

Answer 1

y =
`(-8)/(3)`x +
`(62)/(3)`

Explanation:

Use slope formula.

then substitute slope for m in y = mx + b

pick a set of coordinates and substitute them in for x and y.

Solve for b

Answer 2

`y=-(8)/(3)x+(62)/(3)`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the points (7,2) and (10,-6)

`m=(2-(-6))/(7-10)\\m=(2+6)/(7-10)\\m=(8)/(-3)`

Therefore, the slope of the line is
`-(8)/(3)`. Plug this into
`y=mx+b`:

`y=-(8)/(3)x+b`

2) Determine the y-intercept (b)

`y=-(8)/(3)x+b`

Plug in one of the given points and solve for b

`2=-(8)/(3)(7)+b\\2=-(56)/(3)+b`

Add
`(56)/(3)` to both sides to isolate b

`2+(56)/(3)=-(56)/(3)+b+(56)/(3)\\(62)/(3)=b`

Therefore, the y-intercept is
`(62)/(3)`. Plug this back into
`y=-(8)/(3)x+b`:

`y=-(8)/(3)x+(62)/(3)`

I hope this helps!