Question 225302
What they've given you here is 2 points:
(-2,3) and (14,-5).
To find the equation, we have to solve for the slope first:
{{{m=(y_1-y_2)/(x_1-x_2)}}}
Plug in the given points:
{{{m=(3-(-5))/(-2-14)}}}
Simplify:
{{{m=8/-16}}}
{{{m=-1/2}}}
Then we can use the following equation:
{{{(y-y_1)=m(x-x_1)}}}
{{{(y-3)=-(1/2)(x-(-2))}}}
Simplify the right hand side:
{{{(y-3)=-(1/2)x-1}}}
Move the -3 over by adding it to both sides:
{{{y=-(1/2)x+2}}}, which is our linear function.
Or, can be written as: {{{f(x)=-(1/2)x+2}}}