Question 136435
You can start with the slope-intercept form of a linear equation: 
{{{y = mx+b}}} where m is the slope and b is the y-intercept.
 Let's find the slope, m, using the slope formula:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} The x's and y's are taken from the two given points: (-3, -2) = ({{{x[1]}}},{{{y[1]}}}) and (-7, -1) = ({{{x[2]}}},{{{y[2]}}}) So, making the appropriate substitution, we get:
{{{m = (-1-(-2))/(-7-(-3))}}} Simplifying,...
{{{m = -(1/4)}}}
So you can start your equation with:
{{{y = (-1/4)x+b}}} Now you need to find the value of b, the y-intercept.
You can do this by substituting the x- and y-coordinate from either of the two given points into the equation above and solving for b.  Let's use the first point (-3, -2) for the x and y.
{{{-2 = (-1/4)(-3)+b}}} Simplify.
{{{-2 = (3/4)+b}}} Subtract {{{3/4}}} from both sides.
{{{-11/4 = b}}}
Now you can write the final equation:
{{{y = (-1/4)x-11/4}}}