Question

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

Through: (-3,-1) and (5,-2)

Answer 1

You first have to find the slope using the slope formula. That looks like this with our values:
`(-2-(-1))/(5-(-3))=- (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(- (1)/(8))+b` and
`-2=- (5)/(8)+b`. Adding 5/8 to both sides and getting a common denominator gives us that
`b=- (11)/(8)`. Writing our slope-intercept form we have
`y=- (1)/(8)x- (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