Which is an equation in point-slope form for the line that passes through the points (-1,4) and (3,-4)?

Question

A. y−3=−2(x+4)
B. y−4=2(x+3)
C. y+4=−2(x−3)
D. y+4=2(x−3)

Answer 1

In order to find the equation of a line, you need a slope and at least one point. When given two points, the slope can be calculated with the equation:

 

m = (y₂-y₁)/(x₂-x₁)

 

where (x₁, y₁) is one point and (x₂, y₂) is the other point.

 

Now, plug in the values from the two points. (Note: it doesn't matter which point you list first or second, as long as you list the values in a consistent order)

 

 

 

m = (y₂-y₁)/(x₂-x₁)

m = (-4 - 4)/(3 - (-1))

m = (-8)/(4)

m = -2

 

or

 

m = (y₂-y₁)/(x₂-x₁)

m = (4 - (-4))/(-1 - 3)

m = (8)/(-4)

m = -2

 

Notice how they both give you the same slope?

 

 

 

 

 

Now that we have a slope and two points, all we have to do is pick a point (either will work), and plug it along with the slope into the point-slope formula:

y-y₁=m(x-x₁)

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

 

 

When we plug in the given values into our formula, we get this:

y-(-4)=-2(x-3)

y+4 = -2(x-3)

 

or

 

y-4 = -2(x-(-1))

y-4 = -2(x+1)

 

 

 

Both equations will produce the same answer when simplified, but in this case, we need to match our answer choice given instead of simplifying.

 

The answer is C