Question

Find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.

1. (4.1) slope = 6

2. (6,-3) slope= -5

3. (-8, 2) slope = -1/2

4. (-7,-1) slope = 0

Answer 1

The slope-point form of a line:

`y-y_0=m(x-x_0)`

The slope-intercept form of a line:

`y=mx+b`

1.

`m=6,\ (4,\ 1)\to x_0=4,\ y_0=1`

Substitute

`y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}`

2.

`m=-5,\ (6,\ -3)`

Substitute

`y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}`

3.

`m=-(1)/(2),\ (-8,\ 2)\\\\y-2=-(1)/(2)(x-(-8))\\\\y-2=-(1)/(2)(x+8)\\\\y-2=-(1)/(2)x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-(1)/(2)x-2}`

4.

`m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}`