find an equation of the line containing the given pair (-1,-6) and (-9,-4)

Question

the equation of the line in slope intercept form is y=

Answer 1

Syd,

 

To find the equation of a line between two points, we first have to find the slope of the line.

 

Use the slope equation:  rise/run  or (y₁ - y₀₎ / (x₁ - x₀)  

 

Make sure to use the two points in the same order each time so: (-4 - (-6))  /  (-9 - (-1))  = 2 / -8  = -1/4

 

Now, plug the slope found and one of the points into the "point-slope" form.

 

That form is is (y - y₀) = m * (x - x₀)

 

(y - (-6)) = -1/4 * (x - (-1))    =>    y + 6 = -1/4(x + 1)     =>   y + 6 = -1/4x - 1/4    

 

Subtract 6 from both sides                                                            - 6              - 6

 

Final equation:      y = -1/4x - 6 1/4    (or -25/4)

 

Test your points:

 

(-6) = -1/4(-1) - 25/4       -6 = -24/4    -6 = -6 √

(-4) = -1/4(-9) - 25/4       -4 = -16/4    -4 = -4 √

Answer 2

With slope intercept form, we need to know the slope of the line m and the intersection point with the y-axis.  To find slope, you measure the difference in y-coordinates and divide by the the difference in x-coordinates of two points on the line.  That is:

 

m = rise/run = (y₂ - y₁)/ (x₂ - x₁) = (-4 - (-6) ) / ( -9 - (-1) ) = (-4 + 6) / (-9 + 1) = 2/(-8) = -1/4.

 

So we know the equation of the line is y = mx+b = (-1/4)x + b.  We just need to find b and we are done.  Since we know two points on the line, we can use either one to find b by substituting the coordinates for x & y.  If we use (-1,-6), we get (the => means implies)

 

y = (-1/4)x + b =>  -6 = (-1/4)(-1) + b => -6 = 1/4  + b => -24/4 = 1/4 + b => -25/4 = b.

 

Thus the equation is y=(-1/4)x - 25/4.

Answer 3

To find the equation of the line, first you need to find the slope between the two points.

 

The slope equation is m = (y₂-y₁)/(x₂-x₁) and your points are (-1,-6) and (-9,-4) so you get

m = (-4 - (-6) )/(-9 - (-1) )

You should be able to simplify this to find m.

The slope intercept form of a line is y = mx + b, where m is the slope you just found and b is the y-intercept, which you do not know. However, you can substitute either of your points in to find it.

y = m x + b

(-6) = (m)(-1) + b

Here you know m from above and can solve for b. Then just rewrite the equation with the m and b that you know in the proper form

y = (m)x + (b)