Question 389093: Find an equation of the line containing the given pair of points.
(4,1) and (12,3) y=
Thank you
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (4,1),(12,3)
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=(3-(1))/(12-(4))
Multiply -1 by each term inside the parentheses.
m=(3-(1))/(12-4)
Subtract 4 from 12 to get 8.
m=(3-(1))/(8)
Multiply -1 by each term inside the parentheses.
m=(3-1)/(8)
Subtract 1 from 3 to get 2.
m=(2)/(8)
Reduce the expression (2)/(8) by removing a factor of 2 from the numerator and denominator.
m=(1)/(4)
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=((1)/(4))*x+b
Substitute the value of x into the equation.
y=((1)/(4))*(4)+b
Substitute the value of y into the equation.
(1)=((1)/(4))*(4)+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.
((1)/(4))*(4)+b=(1)
Multiply ((1)/(4)) by (4) to get ((1)/(4))(4).
((1)/(4))(4)+b=(1)
Remove the parentheses around the expression 1.
((1)/(4))(4)+b=1
Multiply (1)/(4) by 4 to get 1.
(1)+b=1
Reorder the polynomial 1+b alphabetically from left to right, starting with the highest order term.
b+1=1
Find the value of b.
b=0
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=(x)/(4)
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