Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
2 answers:
Answer:
5x - 3y = 30
Step-by-step explanation:
First we find the slope of the line using the formula
Using our points, we have
m = (-5-0)/(3-6) = -5/(-3) = 5/3
Next we write the equation using point-slope form. Using the slope of 5/3 and the second point, we have
y-0 = 5/3(x-6)
y = 5/3(x-6)
Using the distributive property, we have
y = 5/3(x)-5/3(6)
y = 5/3(x)-5/3(6/1)
y = 5/3(x)-30/3
y = 5/3x - 10
We cannot have fractions in standard form. To deal with this, we will multiply all 3 terms by 3:
3y = 5/3x(3) - 10(3)
3y = 5x - 30
We want x and y on the same side; subtract 5x from each side:
3y-5x = 5x-30-5x
-5x+3y = -30
We want x to be positive; multiply all 3 terms by -1:
5x-3y = 30
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that means we are free to pick any number for x that is between -5 and 3, including 3.
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Now we join those points by a curved line.
means we use a close circle at -5
x<3 means use open circle at 3
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Repeat same process for 2nd part f(x)=x-4
choose any number between 3 and 7 like x=3, 4 etc
so we get points (3,-1), (4,0) etc
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