Functions and lines - Linear funcations
18 important questions on Functions and lines - Linear funcations
Give an equation , we can find an equivalent equation
2. Multiplying or dividing both sides by the same nonzero quantity
Linear equations in two variables
where A, B, and C are constants and A and B are not both 0.
A soluation to a linear equation in two variables
the solution set is the set of all solutions of the equation.
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Graph of linear equation
Horizontal and vertical lines
x=0
How to sketch the graph
Find the slope that passes through the points (-3,1) and (3,-5) ?
What is the rate of change of the population?
Sketch graph based on standard form/ slope intercept form y=3x-2
- Y intercepts are (0,-2)
- slope 3
- 3-2 = 1
Find the equation of the line passing through (-1,3) and (2,1)
- Find first m
- write the points and m in point-slope form
- then re-write in standard in standard form
- find first m
- write in standard form and find b
Linear equation application in business
Assume that daily total cost c is linearly related to daily production level x.
1. Find the equation realting to cost of production of the form C=mx+b
2. If production increases to 80 widgets per day, what will the total cost of production per day be ?
A comapny plans to begin manfcaturing a new model of hairdryer. In order to do this, they must first purchase $20,000 of new equipment. Afterwards, the cost of producing each hairdryer ( supplies and labour) is $ 17.
Find a formula for the total cost C(x0 of producing x hairdryers.
What is the total cost of producing 125 hairdryers ?
Parallel and perpendicular lines
pependicular -2 = 1/2
Find the equation of line perpendicular to y=3/2-3 passing through the point (6,1)
y-1=-2/3(x-6)
y-1=-2/3x+4
y=-2/3x+5
Find the point of intersecation of the lines y=4x-1 and y=11-2x
6x=12
x=2
2. Y=4x-1
= 4(2)-1
= 7
3.(2,7)
Rember : if we multiplay or dvide by number, then we must reverse the inequality.
Interval notation and inequality
- Interval notation
A golf course charges $52 for a round of golf using a set of their clubs, and $ 44 if you have your own clubs. If a set of clubs cost $270, how many rounds of golf must you play in order to make it more cost-effective to buy your own clubs?
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