# Week 3 Mat221

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...

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