Assignment 18

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course Mth158

3-27 7pm

018. `* 18

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Question: * 2.3.34 / 30 (was 2.3.24). Slope 4/3, point (-3,2)

Give the three points you found on this line and explain how you obtained them.

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Your solution:

To find another point, move 4 units up the y axis and 3 units across the x axis

(0, 6) is the point reached

You can also use the slope -4/-3 to find points

So we move 4 points down the y axis or add -4 to 2, and move 3 units backward across the x axis or add -3 to -3

The point is (-6, -2)

For a third point, we can use (0, 6) and add the values from the slope 4/3 to get

(3, 10)

confidence rating #$&*:3

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Given Solution:

* * STUDENT SOLUTION:

(-3,2) slope 4/3. Move 3 units in the x direction, 4 in the y direction to get

((-3+3), (2+4)), which simplifies to

(0,6)

(-3,2) slope 4/3 = -4/-3 so move -3 units in the x direction and -4 in the y direction to get

((-3-3), (2-4)) which simplifies to

(-6,-2)

From (0,6) with slope 4/3 we move 4 units in the y direction and 3 in the x direction to get

((0+3), (6+4)), which simplifies to

(3,10). The three points I obtained are

(-6,-2), (0,6), (3,10).

* 2.3.40 / 36 (was 2.3.30). Line thru (-1,1) and (2,2) **** Give the equation of the line and explain how you found the equation.

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Your solution:

First find the slope of the line

Using the slope formula, m = (y^2 - y^1)/(x^2 - x^1)

This give us the slope 1/3

Now we use the point slope equation- y - y^1 = m(x - x^1), using slope 1/3 and point (-1,1) and solve for y

This give us the equation

Y = 1/3 x + 4/3

confidence rating #$&*:3

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Given Solution:

* * STUDENT SOLUTION: The slope is m = (y2 - y1) / (x2 - x1) = (2-1)/(2- -1) = 1/3.

Point-slope form gives us

y - y1 = m (x - x1); using m = 1/3 and (x1, y1) = (-1, 1) we get

y-1=1/3(x+1), which can be solved for y to obtain

y = 1/3 x + 4/3.

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Self-critique (if necessary):ok

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Self-critique Rating:3

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Question: * 2.3.54 / 46 (was 2.3.40). x-int -4, y-int 4 * * ** What is the equation of the line through the given points and how did you find the equation?

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Your solution:

The two points are (0, 4) and (-4, 0)

You can find the equation of the line using slope intercept form

Y = mx + b, b representing the y intercept

So we have

Y = -x + 4

confidence rating #$&*:3

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Given Solution:

* * STUDENT SOLUTION: The two points are (0, 4) and (4, 0). The slope is therefore m=rise / run = (4-0)/(0+4) = 1.

The slope-intercept form is therefore y = m x + b = 1 x + 4, simplifying to

y=x+4.

STUDENT QUESTION

I obtained

-x + y = 4 or y = x + 4.

I followed the example in the book which leaves 2 solutions (example problem 2.3.51) Did I do it correctly?

INSTRUCTOR RESPONSE

Both your solutions represent the same line, and both are correct.

y = 1x + 4 means the same thing as y = x + 4; we rearrange this to -x + y = 4 (just subtract x from both sides).

• -x + y = 4 is a 'standard form' of the equation of this line.

• y = x + 4 is the 'slope-intercept' form of the equation.

You don't need to know this, but still another 'standard form' is obtained by subtracting 4 from both sides of the equation -x + y = 4, giving us

-x + y - 4 = 0.

In this form we often want the coefficient of x to be positive, so we multiply both sides by -1 to get

x - y + 4 = 0.

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Self-critique (if necessary): I felt very confident about my answer, but in the given solution, the x intercept is listed as (4, 0) when in the question it states that the x intercept is -4…my solution is based on the x intercept being -4.

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Self-critique Rating:3

@&

The student solution mistakenly listed one of the points as (0, 4). That should have been (0, -4).

Had the point been (0, 4) the slope would have been (4 - 0) / (0 - 4) = -1.

The point was (0, -4), so the slope was in fact (4 - 0) / (0 - (-4) ) = (4 - 0) / (0 - 4) = 1.

So when the student said that the slope was

(4 - 0) / (0 - 4) = 1

he or she was at this point correct.

The correct equation of the line is therefore

y = m x + b = 1 x + 4, or just

y = x + 4.

*@

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Question: * 2.3.76 / 56 (was 2.4.48). y = 2x + 1/2. **** What are the slope and the y-intercept of your line and how did you find them?

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Your solution:

confidence rating #$&*:

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The y intercept is (0, ½)

The slope is m=2

You can find both using the slope intercept form y = mx + b, in which case m=slope and b= y-intercept

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Given Solution:

* * the y intercept occurs where x = 0, which happens when y = 2 (0) + 1/2 or y = 1/2. So the y-intercept is (0, 1/2).

The slope is m = 2.**

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Self-critique (if necessary):ok

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Self-critique Rating:3

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Question: * 2.3.62 / 22 (was 2.4.18) Parallel to x - 2 y = -5 containing (0,0) **** Give your equation for the requested line and explain how you obtained it.

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Your solution:

Solve x - 2y = -5 for y

Y= ½ x + 5/2

So the line parallel to this line will have a slope of ½

We can use point slope form with the given point (0, 0) to get the equation

Y - 0 = ½(x - 0) or

Y = 1/2x

confidence rating #$&*: 3

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Given Solution:

* * The equation x - 2y = -5 can be solved for y to give us

y = 1/2 x + 5/2.

A line parallel to this will therefore have slope 1/2.

Point-slope form gives us

y - 0 = 1/2 * (x - 0) or just

y = 1/2 x. **

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Self-critique (if necessary):ok

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Self-critique Rating:3

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Question: * 2.3.68 / 28 (was 2.4.24) Perpendicular to x - 2 y = -5 containing (0,4) **** Give your equation for the requested line and explain how you obtained it.

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Your solution:

Solve the equation for y to get slope intercept form

Y = 1/2x + 5/2

Lines perpendicular to each other will have slopes that multiply to reach a product of -1

So the slope of this line will be -2

With the slope of the second line and the given point (0, 4), we can use point slope form to get our equation

Y - 4 = -2(x - 0)

Solve for y

Y -4 = -2x

Y= -2x + 4

confidence rating #$&*: 3

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Given Solution:

* * The equation x - 2y = -5 can be solved for y to give us

y = 1/2 x + 5/2.

A line perpendicular to this will therefore have slope -2/1 = -2.

Point-slope form gives us

y - 4 = -2 * (x - 0) or

y = -2 x + 4. **

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Self-critique (if necessary):ok

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Self-critique Rating:3

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Question: * 2.3.68 / 28 (was 2.4.24) Perpendicular to x - 2 y = -5 containing (0,4) **** Give your equation for the requested line and explain how you obtained it.

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Your solution:

Solve the equation for y to get slope intercept form

Y = 1/2x + 5/2

Lines perpendicular to each other will have slopes that multiply to reach a product of -1

So the slope of this line will be -2

With the slope of the second line and the given point (0, 4), we can use point slope form to get our equation

Y - 4 = -2(x - 0)

Solve for y

Y -4 = -2x

Y= -2x + 4

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

* * The equation x - 2y = -5 can be solved for y to give us

y = 1/2 x + 5/2.

A line perpendicular to this will therefore have slope -2/1 = -2.

Point-slope form gives us

y - 4 = -2 * (x - 0) or

y = -2 x + 4. **

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Self-critique (if necessary):ok

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Self-critique Rating:3

#*&!

&#This looks good. See my notes. Let me know if you have any questions. &#