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Question 391298: write an eaquation of the direct variation that includes the given points (2,3) and (-5,-7).
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (2,3),(-5,-7)
Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.
To calculate the equation of the line, use the y=mx+b format.
Slope is equal to the change in y over the change in x, or 'rise over run'.
m=(change in y)/(change in x)
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=(y2-y1)/(x2-x1)
Substitute in the values of x and y into the equation to find the slope.
m=(-7-(3))/(-5-(2))
Multiply -1 by each term inside the parentheses.
m=(-7-(3))/(-5-2)
Subtract 2 from -5 to get -7.
m=(-7-(3))/(-7)
Move the minus sign from the denominator to the front of the expression.
m=-((-7-(3))/(7))
Multiply -1 by each term inside the parentheses.
m=-((-7-3)/(7))
Subtract 3 from -7 to get -10.
m=-((-10)/(7))
Move the minus sign from the numerator to the front of the expression.
m=-(-(10)/(7))
Multiply -1 by each term inside the parentheses.
m=(10)/(7)
Find the value of b using the formula for the equation of a line.
y=mx+b
Substitute the value of m into the equation.
y=((10)/(7))*x+b
Substitute the value of x into the equation.
y=((10)/(7))*(2)+b
Substitute the value of y into the equation.
(3)=((10)/(7))*(2)+b
Since b is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
((10)/(7))*(2)+b=(3)
Multiply ((10)/(7)) by (2) to get ((10)/(7))(2).
((10)/(7))(2)+b=(3)
Remove the parentheses around the expression 3.
((10)/(7))(2)+b=3
Multiply (10)/(7) by 2 to get (20)/(7).
((20)/(7))+b=3
Reorder the polynomial (20)/(7)+b alphabetically from left to right, starting with the highest order term.
b+(20)/(7)=3
Find the value of b.
b=(1)/(7)
Now that the values of m(slope) and b(y-intercept) are known, substitute them into y=mx+b to find the equation of the line.
y=(10x)/(7)+(1)/(7)
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