Question

for which value of k are the points (0 -5) (6 k) and (-4 -13) collinear?

Answer 1

Answer:

Step-by-step explanation:

Use the 2 points for which you have both an x and y coordinate to write the equation of the line containing those 2 points.  When you get the equation, sub in the x value of 6 and solve for y.  

Begin by finding the slope of the line:

$m=\frac{-13-(-5)}{-4-0}=\frac{-13+5}{-4}=\frac{-8}{-4}=2$

Then use one of the points in point slope form to write the equation in slope-intercept form.  I used (0, -5).  But either point you choose will give you the exact same line...promise.

y - (-5) = 2(x - 0) and

y + 5 = 2x and

y = 2x - 5

Now sub in the x value of 6 for x and solve for y:

y = 2(6) - 5 and

y = 12 - 5 so

y = 7