Compare and contrast point-slope form with slope-intercept form. Also, state what type of problem is each one is best to use to solve.

Question

This is for my math homework---i have to answer in 5 sentences at least.

Answer 1

y=mx + b is the general equation for a line in slope intercept form. it can be rewritten in point slope form

y-b=m(x-0) where the y intercept is the point (0,b)

y-h=m(x-k) is the general equation for a line in point slope form with m=slope and (k,h) a point on the line

It can be rewritten in slope intercept form by solving for y and combining constant terms

y = mx-mk + h, in this form h-mk = b = the y intercept

In economic problems, such as ones with a linear demand curve, the y intercept tells you the price that makes consumers stop buying altogether. for demand curves slope is always (or in practical situations) negative.

But generally, you don't have the y intercept or the slope, but only a couple points. Using those points in point slope form gives you the demand curve equation: two points (Q,P) such as (20,10) (15,30) can be plugged into an equation (30-10)/15-20) = 20/-5 = -4 = slope of the demand curfve

(y2-y1)/(x2-x1) = m with points (x1,y1) = (15,30) and (x2,y2) = (20,10) then the equation can be written using just one point and the slope

y-10 = -4(x-20) or for economics P=y = price and Q=x = quantity demanded

P-10 =-4(Q-20)