Question

A straight line intersects the curved graph y=x^2-4x at the point where x=-1 and x=-2. Work out the equation of the straight line.

Answer 1

y = -7x - 2 Use the two points given to find the slope (m) m = (y2 - y1) / (x2 - x1) m = ( 12-5 ) / (-2 - (-1)) m = -7 Now we have y = -7x + b where 'b' is our y-intercept. We can solve for 'b' by choosing one of the (x,y) coordinate points and plugging them in. Let's choose the point (-1,5). Plug -1 in for 'x' and 5 in for 'y' and solve for 'b'. y = -7x + b 5 = -7(-1) + b b = -2 Final eqn: y = -7x - 2

Answer 2

Where x=-1:
Y= (-1)^2 - 4(-1)
Y= 1 - -4
Y= 5

Where x=-2:
Y= (-2)^2 - 4(-2)
Y= 4 - - 8
Y= 12

Now we calculate the gradient/slope:

m= y2-y1/x2-x1
m= (12 - 5)/(-2 - -1)
m= 7/-1

Finally, the y-intercept:

y= -7x + c
Using any of the known points from earlier (-1,5) or (-2,12)
5= -7(-1) + c
5 -7 = (7 - 7) + c
-2 = c

The equation is y = -7x - 2