Find the equation of an line thru the given points. answer in slope intercept-form.(-2,,-7)(4,-4)

Question

Finding the slope-intercept form of these numbers.

Answer 1

m = ( -4 - (-7)) / ( 4 - (-2)) = 3/ 6 = 1/2

 

 

Y = mx +b

 

 Y = 1/2 X + b

 

It passes through ( -2, -7) ( 4, -4)

 

    Therefore:

 

    -7 = 1/2( -2) +b 

 

     b = -6

 

  Y = 1/2X - 6

 

   If you have other point ( 4. -4) will give you the same answer.

 

 

Answer 2

Slope-intercept form of a line: y - y₀ = m(x - x₀)

 

The slope of a line is the "rise" (change in y) divided by the "run" (change in x).  For this problem, the change in y between the two points is (-4) - (-7) = 3; the change in x is (4) - (-2) = 6.  These are examples of the general formula for change in a variable: Δx = (x₂) - (x₁).  The slope is then 3/6 which simplifies to 1/2.  In this equation the slope is represented by the variable m.

 

Then you just plug the x- and y-values for one of the points on the line into x₀ and y₀ in the formula.  Any point will work, including the two that were given in the problem.