Answer:
[tex]y = - \frac{1}{5} x - 1[/tex]
Step-by-step explanation:
Choose any 2 points on the line indicated by dots. I'll choose (5,-2) and (10,-3)
work out the gradient between these two points.
equation:
[tex] \frac{change \: in \: y}{change \: in\: x} = gradient[/tex]
[tex] \frac{ - 3 - ( - 2)}{10 - 5} = - \frac{1}{5} [/tex]
the gradient is -1/5
the equation we need to write it in is y=mx+c. use one of the two coordinates chosen. I'll use (5,-2). y is -2, m is the gradient which is -1/5 and x is 5.
working out c:
[tex]y = mx + c [/tex]
[tex] - 2 = - \frac{1}{5} (5) + c[/tex]
[tex] - 2 = - 1 + c \\ [/tex]
add one to both sides.
C is -1
we now have c and the gradient, so the equation is
[tex]y = - \frac{1}{5} x - 1[/tex]
