I don't understand slopes???

Question

I know this is asking alot but my teacher is not answering her test and my mom is yelling at me because of that... Please help me with these problems I'm haveing trouble with them...

Choose the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7.

(1,-1)

(-1,1)

(-1,-1)

(1,1)

Choose the orderred pair that is the solution to the following system of equations: -3x + y = 4 and -7x + y = 12.

(-2,-2)

(-2,2)

(2,-2)

(2,2)

Choose the ordered pair that is the solution to the following system of equations: y= 2x + 1 and y = x -5.

(-6, -1)

(-6,-11)

(4,9)

(4,-1)

Choose the equation of the line passing through the points (3,4) and (1,-6).

y = 5x - 19

y = (1/5)x + 15/5

y = (1/5)x - 2

y = 5x - 11

Choose the equation of the vertical line passing through the point (-2,1).

x = -2

x = 1

y = -2

y = 1

Choose the equation of the line passing through the points (-2,3) and (-4,1).

y = x -1

y = (-1/3)x + 7/3

y= x-4

y = x + 5

Choose the equation of the line with a slope of 2/3 and y passing through the point (6,-2).

y= (2/3)x -6

y= (2/3)x -2

y= (2/3) x -4

y = (3/2) x -6

Choose ALL the points that are solutions to the equation y= 2x -5.

(0,-5) ( I think its this 1)

(1,3)

(-1,-7) (this one)

(1/2, -4) (and this 1)

Find the y intercept of the graph represented by the equation 3x + 4y = 12.

(0,3) ( I think its this 1)

(3,0)

(4,0)

(0,4)

Find the x intercept of the graph represented by the equation 3x + 4y = 12.

(0,3)

(3,0)

(4,0) ( I think its this 1)

(0,4)

Choose the equation that is written in standard form.

y= -3x +4

2y = x+8

x = 3y-6

4x -2y = 10 ( I think its this 1)

What is the slope of the line y= -3?

Zero

Undefined

-3 ( I think its this 1)

Not enough information.

What is the slope of the line x=2?

Zero

Undefined

2 ( I think its this 1)

Not enough information.

Choose the best directions for graphing the equation y= (1/2)x + 1.

Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line.

Graph the point (1,0) and count to the right 1 and up 2 to find another point on the line.

What is the y intercept of the equation y= (2/3)x -6?

2/3

6

-6

No y intercept

In the equation y=-2x +5, name the slope and the y intercept.

slope 1/2, y intercept 5

slope -2, y intercept 5

slope 5, y intercept -2

slope 5, y intercept 1/2

What is the slope of the line with equation y = (1/2)x -3?

1/2

-3

2

-2

Put the following equation in slope intercept form 2x - 5y = 10.

x-y = (-2/5)x-2

y = (-2/5)x + 2

y = -2x + 10

y = (2/5)x -2

What is the slope of the line containing the points (-1,4) and (3,2)?

-2

1/2

-1/2

2

Answer 1

1) Choose the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7.

Ans: (1,1)

Explanation: 5x - 2y = 3 ----------(1)

3x + 4y = 7 ----------(2)

Multiply (1) by 2

10x - 4y = 6 ---------(1) * 2

3x + 4y = 7 ---------(2)

____________________

Add: 13x = 13

Or, x = 1

Put x = 1 in (1)

5*1 - 2y = 3

Or, 5 - 2y = 3

Or, 2y = 2

Or, y = 1

Questions 2,3,4 have been answered by somebody else.

5)Choose the equation of the vertical line passing through the point (-2,1).

Ans: x = -2

6) Choose the equation of the line passing through the points (-2,3) and (-4,1).

Ans: y = x + 5

Explanation:

y - y1 = {(y2 - y1)/(x2 - x1)}(x - x1)

y - 3 = {(1 - 3)/(-4 + 2)}(x + 2)

y - 3 = (-2/-2)(x + 2)

y - 3 = x + 2

y = x + 5

7) Choose the equation of the line with a slope of 2/3 and y passing through the point (6,-2).

Ans: y = (2/3)x - 6

Explanation:

y -(-2) = (2/3)(x - 6)

Or, y + 2 = (2/3)x - (2/3)*6

Or, y + 2 = (2/3)x - 4

Or, y = (2/3)x - 6

8) Choose ALL the points that are solutions to the equation y= 2x -5

Ans: your answer is correct

9) Find the y intercept of the graph represented by the equation 3x + 4y = 12.

Ans: your answer is correct

10) Find the x intercept of the graph represented by the equation 3x + 4y = 12.

Ans: your answer is correct

11) Choose the equation that is written in standard form.

Ans: your answer is correct

12) What is the slope of the line y= -3?

Ans: Zero

13) What is the slope of the line x=2?

Ans: Undefined

14) Choose the best directions for graphing the equation y= (1/2)x + 1.

Ans: Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line.

15) What is the y intercept of the equation y= (2/3)x -6?

Ans: -6

16) In the equation y=-2x +5, name the slope and the y intercept.

Ans: slope -2, y intercept 5

17)What is the slope of the line with equation y = (1/2)x -3?

Ans: 1/2

18) Put the following equation in slope intercept form 2x - 5y = 10.

Ans: y = (2/5)x - 2

Explanation: 2x - 5y = 10

Or, 5y = 2x - 10

Or, y = (2/5)x - 2

19) What is the slope of the line containing the points (-1,4) and (3,2)?

Ans: -1/2

Explanation: If a line joins (x1, y1) and (x2, y2), then

slope = (y2 - y1)/(x2 - x1)

Slope = (2 - 4)/{3 -(-1)} = -2/4 = -1/2

Answer 2

jeez, looking over the answers, I guess they are all right.  But, if your title is right ("I don't understand slopes"), all those answers wouldn't help me much.

You've got a buncha answers.  Now here's my 2 cents worth--

--there's no simple way to do problems like these.

--know that slope just means "slope". A vertical line doesn't slope, so we usually say it's slope is zero.  A horizontal line's slope is usually said to be "undefined"   ...other lines slope, like a hillside or a roof.

--in the world outside the math class, 'slope' means run over rise.  A carpenter will measure slope of a roof by measuring how much the roof rises (or falls) per foot of horizontal 'run'.

--in math class, slope is how much difference in 'x', divided by change in'y'...so for your last one, change in x is 3-(-1), or 4, and change in y is 2-4, or -2 and slope is 4/-2 or -2.

--back to rule 1, 'there's no simple way...', meaning that you must, like in your first one, actually calculate the slope of 5x-2y=3 AND 3x + 4y =7 by inserting each pair, a pair at the time, into both equation.  This is usually done in your head...it just takes too long on paper.  KEY:  the "solution" means BOTH lines have one point in common and you gotta find it...

Lotsa luck, it don't get easier.  But remember this.  You're learning to use the tools of mathematics, just like the mechanic has to learn to use a wrench and pliers.  It doesn't get any easier, it it do get funner.

Answer 3

I'll give you the answers. But I can't explain all the solution here.

1) (1, 1)

2) (-2, -2)

3) (-6, -11)

4) y = 5x - 11

5) x = -2

6) y = x + 5

7) y= (2/3)x -6

8) (0,-5)

    (-1,-7)

    (1/2, -4)

9) (0,3)

10) (4,0)

11)  4x -2y = 10

12)  Zero  ---> remember that y = -3 is a horizontal line

13)  Undefined -----> this is a vertical line

14)   Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line.

15)  -6

16)  slope -2, y intercept 5

17) 1/2

18)  y = (2/5)x -2

19)  1/2  

Answer 4

case 1:

5x - 2y = 3   [ 3]  --> 15x - 6y = 9

3x + 4y = 7  [ 5]  --> 15x + 20y = 35

so : y = 26/26 = 1 , x = 1  or [1,1]

case 2:

-3x + y = 4

-7x + y = 12.

so x = -8/4 = -2 , x = -2 or [-2,-2]

case 3:

y= 2x + 1

y = x -5

so 2x + 1 = x -5 --> x = -6 , y = -11  or [-6,-11]

case 4:

(3,4) and (1,-6).

[y - 4]/[x - 3] = [1 - 4]/[-6 - 3] = -1/3

y = -1/3[x - 3] + 4

y = -1/3x + 5

case 5:

x = -2

case 6:

Answer 5

(1,1)

(-2,-2)

(-6,-11)

sry i have to go to work but theres the first 3

Answer 6

To find the ordered pair that is the solution to a system of equations, pick the point that works for both equations.