Question

How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line D (3, -7) (9,-3)?

Answer 1

Slope is `2/3` , point slope form is `y+7=2/3(x-3)`,
slope-intercept form is `y= 2/3x-9.`, standard form is
`2x-3y=27`.Domain: `x in RR or (-oo,oo)`. Range: `y in RR or (-oo,oo)`

Explanation:

The slope of the line passing through `(3,-7) and (9,-3)` is

`m= (y_2-y_1)/(x_2-x_1)= (-3+7)/(9-3)=4/6=2/3`

Point slope form of the line is `y-y_1=m(x-x_1)` or

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

Let the equation of the line in slope-intercept form be `y=mx+c`

or `y=2/3x+c` . The point (3,-7) will satisfy the equation . So,

`-7= 2/3*3+c or c= -7-2= -9`. Hence the equation of

the line in slope-intercept form is `y= 2/3x-9.`

The equation of the line in standard form is `3y=2x-27` or

`2x-3y=27`.

Domain of the line `y= 2/3x-9.` is any real value of `x`

Domain: `x in RR or (-oo,oo)`

Range of the line `y= 2/3x-9.` is any real value of `y`

Range: `y in RR or (-oo,oo)`

graph{2/3x-9 [-40, 40, -20, 20]}