Write in slope-intercept form an equation of the line that passes through the points (-5,6)(-5,6) and (3,-10)(3,-10).

Question

i need help with this qustion because i just dont understant it

 

Answer 1

The problem gives two points:    (-5,6) and (3,-10).

 

In the Cartesian Coordinate System, we plot points (x,y) on two axes.

 

Two points determine a line.  When you connect them -- and keep on going -- that line has an equation that the problem asks you to find.

 

The slope-intercept form of the equation a line looks like:  y=mx + b

     where m is the slope

      and the point (0,b) is the y-intercept [the point where the line crosses the y-axis -- at x=0]

 

Given two points (x₁,y₁) and (x₂,y₂) the equation of the line is:

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

 

     y - 6   = ( (-10 - 6)/(3 -(-5)) ) (x - (-5))

     y - 6   =  ( (-16)/(8) ) (x + 5)

     y - 6   =    -2 (x+5)

     y - 6   = -2x -10

        y = -2x -4

 

Check to see whether both points are on the line (that is, they both satisfy the equation):

  Is  6 = -2(-5) -4   ?

       6 = 10 - 4   ?

       6 = 6   ?yes

  Is  -10 = -2(3) - 4   ?

        -10 = -6 - 4   ?

        -10 = -10   ?yes

 

Answer 2

The slope-intercept equation for a line is y = mx + b.  The slope is "m" and "b" is where the line intercepts the y-axis.  If you plot the points (-5,6) and (3, -10)and draw a line you can see the line slopes down and you can see the y-intercept.

 

To solve for the slope, you take the change in Y divided by the change in X.  The change is y is -10 -6 = -16.  The difference between the y of the second point minus the y of the first point.  The change in x is 3 - -5 = 8.  So -16/8 = -2. 

 

Then you can find "b" by substituting one of the points for x and y.  So if you use the point (-5,6) the equation is

6 = (-5)(-2) + b. 

6 = 10 + b

b = -4

 

The equation is y = -2x-4.