Question

Write the standard form of the equation of the line through the given points.

Answer 1

You first have to find the slope using the slope formula.  That looks like this with our values:  $\frac{-2-(-1)}{5-(-3)}=- \frac{1}{8}$.  So the slope is -1/8.  Use one of the points to first write the equation in y = mx + b form.  We have an x and a y to use from one of the points and we also have the slope we just found.  Filling in accordingly to solve for b gives us $-2=5(- \frac{1}{8})+b$  and  $-2=- \frac{5}{8}+b$.  Adding 5/8 to both sides and getting a common denominator gives us that  $b=- \frac{11}{8}$.  Writing our slope-intercept form we have $y=- \frac{1}{8}x- \frac{11}{8}$.  Standard form for a line is Ax + By = C...no fractions allowed.  So let's get rid of that 8 by multiplying each term by 8 to get 8y = -x - 11.  Add x to both sides to get it into the correct form:  x + 8y = -11