what equation in slope intercept form represents the line that passes through the points (-3,4) and (2,-1)?

Question

Can someone please help me

Answer 1

The equation of the line has a form of y=mx+b, where m- slope, b is the y-intercept. First , find slope using the coordinates of the 2 points: m=(y2-y1)/(x2-x1)

m=(-1-4)/(2-(-3))=(-5)/(2+3)=-5/5=-1

Now we know, that partial equation of the line will be 

y=(-1)x+b or 

y=-x+b

Now, using the coordinates of either point, we can find b by substituting x and y in the partial line equation. Let's say we use the point (-3,4), therefore x=-3, y=4. Substitute into y=-x+b

4=-(-3)+b

4=3+b

solve for b

b=4-3=1

therefore, the line equation is

y=-x+1

Check using 2nd point's coordinates (2,-1)--> x=2, y=-1

-1=-2+1

-1=-1

Answer: y=-x+1

Answer 2

You need to know the point slope form, since you are given 2 points.  You also need to figure out the slope.  Slope is change in y over change in x:

 

(y1-y2)/(x1-x2) = (4--1)/(-3-2) = 5/-5 = -1  (Note this could also be found with (-1-4)/(2--3) )

 

With the slope, you can use EITHER point to get your line equation.  I'll show you with both.

 

The point slope form is y-y1 = m(x-x1)

 

Using (-3,4)

y-4 = -1(x--3) (set up)

y-4 = -1 (x+3) (simplify)

y-4 = -x-3 (distribute -1)

y = -x+1 (add 4 to both sides)

 

Using (2,-1)

y--1 = -1(x-2) (set up)

y+1=-x+2 (simplify and distribute -1)

y=-x+1 (subtract 1 from both sides)

 

Notice the final result is the same for either point.  

Answer 3

Use the two-point form:

 

(y - y₁)/(x - x₁) = (y₁ - y₂)/(x₁ - x₂)

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

(y - 4)/(x + 3) = 5/-5

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

y - 4 = -1(x + 3

y - 4 = -x - 3

y = -x - 1