Question

a line segment has the endpoint (2,-3) (-6,-1) Describe theOff the line that through the points ex and Y

Answer 1

Explanation:

The point-slope form of an equation of a line:

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

where the slope m is:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (2, -3) and (-6, -1).

Substitute:

`m=(-1-(-3))/(-6-2)=(2)/(-8)=-(1)/(4)`

`y-(-3)=-(1)/(4)(x-2)\\\\y+3=-(1)/(4)(x-2)\to\text{point-slope form}`

The slope-intercept form of an equation of a line:

`y=mx+b`

`y+3=-(1)/(4)(x-2)`

`y+3=-(1)/(4)x+(1)/(2)` subtract 3 from both sides

`y=-(1)/(4)x-2(1)/(2)\to\text{slope-intercept form}`

The standard form of an equation of a line:

`Ax+By=C`

`y+3=-(1)/(4)(x-2)` multiply both sides by 4

`4y+12=-(x-2)`

`4y+12=-x+2` subtract 12 from both sides

`4y=-x-10` add x to both sides

`x+4y=-10\to\text{standard form}`