Question

A line passes through the points (6,5) and (2,2) . Select Yes or No to tell whether each equation describes this line. Equation Yes No y−5=34(x−6) y−5=−43(x−2) y−2=−34(x−6) ​y−2=34(x−2)​

Answer 1

`y-5=(3)/(4)(x-6)`,Yes

`y-5=-(4)/(3) (x-2)`,NO

`y-2=-(3)/(4) (x-6)`,NO

`y-2=(3)/(4)(x-2)`,Yes

Step-by-step explanation

The line passes through these two points,
`(6,5)` and
`(2,2)`.

We can use these two points to determine the slope of the line.

The formula for finding the slope of a line when at least two points are known is
`m=(y_2-y_1)/(x_2-x_1)`.

We can choose
`(x_1,y_1)=(6,5)` and
`(x_2,y_2)=(2,2)` or
`(x_1,y_1)=(2,2)` and
`(x_2,y_2)=(6,5)`.

We shall get the same result.

`m=(2-5)/(2-6) =(-3)/(-4) =(3)/(4)`.

We now determine the equation of the line using the poit-slope formula,

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

When we choose
`(x_1,y_1)=(6,5)`, then we will obtain,

`y-5=(3)/(4)(x-6)` as the point-slope form.

When we choose
`(x_1,y_1)=(2,2)`, then we will obtain,

`y-2=(3)/(4)(x-2)` as the point-slope form.