Question 117593
write an equation in standard form for the given information
(9,4),m=-1/3
In the slope/intercept form y = mx + b:
y = {{{-1/3}}}x + b
Substitute for x & y and find b
4 = {{{-1/3}}}(9) + b
4 = -3 + b
4 + 3 = b
b = 7
Therefore we have the slope intercept equation:
y = {{{1/3}}}x + 7
Get rid of the fraction multiply by 3
3y = -x + 21
Arrange in the standard form, add x to both sides
x + 3y = +21; check equation by substituting the given values for x and y
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(-3,-1) (2,-2)
Find the slope using the slope equation: m = {{{((y2-y1))/((x2-x1))}}}
x1 = -3; y1 = -1; x2 = 2; y2 = -2; substitute in the slope equation:
m = {{{((-2-(-1)))/((2-(-3)))}}} = {{{((-2+1))/((2+3))}}} = {{{-1/5}}}
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Use the slope/intercept equation again
y = {{{-1/5}}}x + b
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Substitute x1 and y1 and find b
-1 = {{{-1/5)}}}(-3) + b
-1 = {{{3/5}}} + b
-{{{5/5}}} - {{{3/5}}} = b
-{{{8/5}}} = b
Therefore we have the point/slope equation (y = mx + b) of:
y = {{{-1/5}}}x - {{{8/5}}}
Multiply by 5 to get rid of the denominator
5y = -x - 8
Convert to standard form
x + 5y = -8; You can check it by substituting the given values for x and y
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A piggy bank contains only quarters and dimes. The total value in the bank is $5.50.
write an equation in standard form that models the possible combinations of nickels and quarters in the piggy bank.
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Let x = no of dimes; Let y = no. of quarters. 
.05x + .25y = 5.50
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They don't like fractions or decimals in the standard form, mult eq by 100
5x + 25y = 550
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