Question

Find the equation of the line that

passes through the given points.
(-5,6.5) and (7, -3.5)

Answer 1

Answer:
`y=-(5)/(6)x+(7)/(3)`

Explanation:

We can create a point-slope form equation with the points given. First, we will find the slope with the slope formula. This finds the change in y over the change in x.

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) ) = (-3.5-6.5)/(7--5) =(-10)/(12) =-(5)/(6)`

Now that we have our slope, we can set up our equation. m is our slope and (x1, y1) is one of the points given. Then we will simplify into a slope-intercept form equation.

Given:

`y-y_1=m(x-x_1)`

Substitute:

`y-6.5=-(5)/(6)(x--5)`

Distribute and change into fractions:

`y-(13)/(2) =-(5)/(6)x-(25)/(6)`

Add
`(13)/(2)` to both sides of the equation :

`y=-(5)/(6)x+(7)/(3)`

I have attached a graph of the given points and this line.