Week 3 Mat221

Write the equation of a line parallel to the given line but passing through the given point.

y=1/2x+1; (4,2)

Locate the parallel Line by using the ordered pair (4,2)
Multiply ½ by x to come up with x/2
Now we have y = x/2 + 1
Let’s use the formula y = mx + b whereas m equals slope and equals the y-intercept.
Right now we know that m = ½ when using the above formula
So in order to find the equation which is parallel to y + 1/2(x + 1) the slopes will have to be equal. We must incorporate the slope of the equation to find the parallel lines by using the point slope formula.
(4, 2) and m = ½
Use formula for equation of a line: m = mx + b
Substitute the value of m into the equation y = 1/2 (x + b)
Add the value for x into the equation y = (1/2)(4) + b
Now put value of y in the equation
2 = (1/2)*(4) + b
Now switch b so it can be on the opposite side of the equation
(1/2) *(4) + b = 2
Multiply ½ by 4 to come up with 2
2 + b = 2
Reorder polynomials b + 2 = 2
Find be value: b = 2-2 b = 0
Finally, to get the equation of the line use the values of the slope (m) and y-intercept (b) in the formula y = mx + b to find the equation of the line.
So the end result is y = x/2

Here is a graph displaying the origin of the parallel lines.

[pic]

Write the equation of a line perpendicular to the given line but passing through the given point. y=-3x-6; (-1,5)
Let’s use the formula y = mx + b slope = m and y – intercept = b
Here m = -3
The negative reciprocal right now is equal to 0. m = 1/3
Find the equation of the line by using the point – slope formula
Use the ordered pair (-1, 5) m = 1/3
Use equation of a line formula: y = mx + b
Put the value of m into the equation: y = 1/3x + b
Put the value of x into the equation: y = 1/3 * -1 + b
Put the value of y into the equation:
5 = 1/3* -1 + b
Place b on the left-side of the equation:
1/3 * -1 + b = 5
Multiply 1/3 by -1 to get -1/3
-1/3 + b = 5
Reorder the