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Question 502673: Write an equation of the line that passes through through the given points.
16. (-5, -4) , (0, 11)
18. (2, 8) , (5, 2)
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 16. (-5,-4),(0,11)
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=(11-(-4))/(0-(-5))
Multiply -1 by the -5 inside the parentheses.
m=(11-(-4))/(0+5)
Adding 0 to an expression does not change the value of the expression.
m=(11-(-4))/(5)
Multiply -1 by the -4 inside the parentheses.
m=(11+4)/(5)
Add 4 to 11 to get 15.
m=(15)/(5)
Cancel the common factor of 5 in (15)/(5).
m=(^(3)15)/(5)
Remove the common factors that were cancelled out.
m=3
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=(3)*x+b
Substitute the value of x into the equation.
y=(3)*(-5)+b
Substitute the value of y into the equation.
(-4)=(3)*(-5)+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.
(3)*(-5)+b=(-4)
Multiply (3) by (-5) to get (3)(-5).
(3)(-5)+b=(-4)
Remove the parentheses around the expression -4.
(3)(-5)+b=-4
Multiply 3 by -5 to get -15.
(-15)+b=-4
Remove the parentheses around the expression -15.
-15+b=-4
Reorder the polynomial -15+b alphabetically from left to right, starting with the highest order term.
b-15=-4
Since -15 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 15 to both sides.
b=15-4
Subtract 4 from 15 to get 11.
b=11
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=3x+11
18. (2,8),(5,2)
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=(2-(8))/(5-(2))
Multiply -1 by the 2 inside the parentheses.
m=(2-(8))/(5-2)
Subtract 2 from 5 to get 3.
m=(2-(8))/(3)
Multiply -1 by the 8 inside the parentheses.
m=(2-8)/(3)
Subtract 8 from 2 to get -6.
m=(-6)/(3)
Move the -1 to the front of the fraction.
m=-(6)/(3)
Move the -1 to the front of the fraction.
m=-((6)/(3)
Cancel the common factor of 3 in (6)/(3).
m=-((^(2)6)/(3))
Remove the common factors that were cancelled out.
m=-(2)
Multiply -1 by the 2 inside the parentheses.
m=-2
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=(-2)*x+b
Substitute the value of x into the equation.
y=(-2)*(2)+b
Substitute the value of y into the equation.
(8)=(-2)*(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.
(-2)*(2)+b=(8)
Multiply (-2) by (2) to get (-2)(2).
(-2)(2)+b=(8)
Remove the parentheses around the expression 8.
(-2)(2)+b=8
Multiply -2 by 2 to get -4.
(-4)+b=8
Remove the parentheses around the expression -4.
-4+b=8
Reorder the polynomial -4+b alphabetically from left to right, starting with the highest order term.
b-4=8
Since -4 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 4 to both sides.
b=4+8
Add 8 to 4 to get 12.
b=12
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=-2x+12
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