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What is the equation of the line that passes through the point (-1, 5) and has a slope of −3?

User EricGS
by
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1 Answer

2 votes

The answer is:

In point slope:


\rm{y-5=-3(x+1)}

In slope intercept:


\rm{y=-3x+2}

Work/explanation:

Given:

  • point : (-1, 5)
  • slope : -3

To find the equation of the line, I'm going to use point slope:


\sf{y-y_1=m(x-x_1)}

Where the slope is m and the point is (x₁, y₁).

So our point-slope is:


\rm{y-5=-3(x-(-1)}

Let's simplify.


\rm{y-5=-3(x+1)}

That's our equation in point slope.

__________________________

We might want to write the equation in slope intercept (y = mx + b).

We can do that, too, but let's simplify first.

We take our point slope equation.

We simplify the right side.


\rm{y-5=-3x-3}

Add 5 on both sides


\rm{y=-3x+2}

This is our equation in slope intercept.

User Lenglei
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7.3k points

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