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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

1 Answer

5 votes

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}

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