Could someone please help me with these one also...I am having a very difficult time...I second guess myself?

Question

1. Find the slope of the line passing through the points (-9,-4) and (0,-4).

2. Find the slope of the line passing through the points (-7,-4) and (-1,-10).

3. Determine which two equations represent parallel lines.
(a). y=5/3x + 4 (b). y= -3/5x -7 (c). y=2x + 8 (d) y=2x -4

4. Find the y- intercept for:
-x + 3y =15

5.Determine which two equations represent perpendicular lines.
(a) y= 4/7x - 3 (b) y=3x-4/7 (c) y= -1/3x + 4/7 (d) y= 1/3x - 4/7

6. Write an equation of the line passing through (4,4) and (4,2).

7. Write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equatin y= -3x+1.

8.Rewrite the equation 2x-3y= -6 as a function of x.

9.Find the slope and y-intercept..... x= -8

10. Find the slope of any line parallel to the line through points (15,1) and (4,2).

Thank those of you in advance for you willingness, effort and help....greatly appreciated...

Answer 1

1: 0, it is a horizontal line
2: -6
3: c and d as the gradients are both 2x
4: the gradient is 5
5: c and d as the gradients (m) are opposite (negative & positive)
6: the answer is undefined as it is a perfectly vertical at 2 along the x-axis.
7: y=3x+5
8: x=1.5y-3
9: you need more information than just the pint of x to find the slope and y intercept
10: -11

i am 100% positive all of these answers are right, you might want to ask your teacher how you do the questions in future because you cant ask these types of questions in the exam, dont stress they are very easy to learn, i am a maths and science tutor so if you feel youre teacher is not good enough i can teach you how to understand these questions as if it is in plain english, my email address is [e-mail], thanks.

Answer 2

Hey hear what, you need to know the formulas...

To find the gradient/slope of a line, it is y*a-y*b/x*a-x*b so for Q1 the workings would read..(-9,-4) is (x*a,y*a) and (0,-4) would be (x*b,y*b)....which is -4-(-4)/0-(-9) but ur ans would be 0.

To figure what two lines are parallel, the gradienst must be equal...hence in Q3 the ans is c and d...note to find when two lines are perpendicular the gradients when multiplied must be equal to -1 hence a and b is perpendicular.

When the equation of the line is in the form y=mx+c, m is always the gradient, y and x represents a point on the line and c is always the intercept on the y axis, so if we put -x+3y=15, by transposing -x we get, 3y=x+15, but you have to divide the right hand side by 3 in order to get rid of the 3 on the left hand side as y is always unitary,hence the sum will be y=x/3 +5.
thus the y intercept is 5.

to get an equation of a line, get the gradient, and when you get the gradient put it in the form, y-y*a=m(x-x*a), don't worry it is not as hard as it looks, the second stage in the equation would be y-4=m(x-4), like i said earlier use any point in the equation, could have also used (4,2)...after that transpose and multiply and put in the form y=mx+c.

for Q7, same thing but the gradient would be 3 as 3 multiplied by -3 is 1 and use the point they give and voila! you will get it.

For q8, make the x the subject of the formula, like how all the time to get the equation of the line we made y the subject, just make x the subject, and transpose and divide as required.

and don't forget, for parallel lines, find the gradient as two lines that are parallel have equal gradients.

Hope this helps.

Answer 3

is this a maths test? heh heh..

1 & 2. (y1 - y2)/(x1 - x2)
3. Use the above formula to get the gradient and see which ones are the same. Those are the parallel lines.
4. Rearrange the equation so that it is equal to x (x=3y +15). Since ur looking 4 the y-int, x is equal to 0, which means, 0=3y+15. Solve it.
5.Find the gradient of each of the equation using the formula in no 1. When a line is perpendicular to another, the product of their gradient would resolve to -1. You can solve it then.
6. Find the gradient first. Write the equation using the gradient form (y=mx + c; where m is the gradient). Find the x-int and you'v got it.
7. Find the gradient of the second eq. Since the eq ur looking for is perpendicular to the second eq, their product would result in -1. Insert the gradient and the intercept into the gradient form.
8. I'v 4gotten bout functions... sorry..
9. By now u should be able to answer this.
10. And this too..

Happy trying! =P

Answer 4

1. this is a horizontal line. slope = 0

2. (y2-y1)/(x2-x1) slope is -6/6 or -1

3. using y=mx+b, where m represents the slope, both c and d have slopes of 2, therefore they are parallel.

4. using y=mx+b, where b represents the y-intercept,
3y=x+15
y= x/3+5
y-intercept is 5

5. perpendicular lines have opposite slopes. none of these have opposite slopes

6. this line is vertical and has an undefined slope. it does not intersect the y-axis at all. therefore the equation would be x=4

7. y=x/3+5 use opposite slope. the opposite of -3 is 1/3

8. using y=mx+b, if we solve for x, the equation would be
x=(y-b)/m
so for 2x-3y=-6
2x=3y-6
x=3y/2-3

9. this is a vertical line. the slope is undefined, and there is no y-intercept.

10. (y2-y1)/(x2-x1) to find slope
(1-2)/15-4)= -1/11
slope = -1/11 and any parallel line will have the same slope

Answer 5

the slope of a line is given by the equation m=(y1-y2)/(x1-x2)
the lines are parallel if they have the same slope so you can try to get the slope of the four lines and see which has the same slope

the lines are perpendicular if they have negative reciprocal slopes for example a line has a slope of 2/3 the line perpendicular to has will have the slope of -3/2

you can write an equation in function of x by transposing all the constant and the terms with the x varaible to the right while the y is in the left for example y=2x+1 here y is a function of x


straight lines has no slopes

if a line x=-8 is given this doesnt mean that it has no y-intercept but rather it has an infinite y coodinate so many that it will be stupudity to name all of them so for simplicity the x coordinate is only given

Answer 6

1. m=(y1-y2)/(x1-x2) , for x1not by x2
m=infinity , for x1=x2
x1=x2=-4 then the slope is infinity and the equation of line is x=-4 parallel with y-axis
2. m=(-10-(-4))/(-1-(-7))=-6/6=-1
3. d1:y=m1x+n1 and d2:y=m2x+n2 is parallel then m1=m2
c and d is parallel ,m1=m2=2
4.3y=x+15 divide by 3
y=(1/3)x+5
5. d1:y=m1x+n1 and d2:y=m2x+n2 is perpendicular lines then m1*m2=-1
b and c is the perpendicular lines (m1*m2=3*(-1/3)=-1)
6.y-y1=m(x-x1) , m=(y2-y1)/(x2-x1) the slope
m=(4-4)/(4-2)=0
the line is: y -4=0 and is parallel with x-axis
7.the slope of line ; -3*m2=-1 , m2=1/3
the line : y-y1= m2(x-x1)
y-5=(1/3)x
y=(1/3)x+5
8.2x+6=3y divide by 3
2/3x+2=y , y=(2/3)x+2
9. the line x=-8 is parallel with y-axis, then the slope is infinity, y is a real number.
10.y-y1=m(x-x1) the parallel line , and m=(y2-y1)/(x2-x1)is the slope
m=(2-1)/(4-15)=-1/11this is the slope.
y-1=-1/11(x-15) this is an line. END!

Answer 7

1)
m = (-4-(-4)) / (-9-0)
m = 0
_____________________________________
2)
m = (-10-(-4)) / (-1-(-7))
m = (-10+4) / (-1+7)
m = -6 / 6
m = -1
_____________________________________
3)
Answer: (c) and (d) because they have the same slope.
_____________________________________
4)
when x=0:
-0+3y = 15
y = 5

when y=0:
-x+3(0) = 15
x = -15

The intercepts are: (0, 5) and (-15, 0)
_____________________________________
5)
Answer: (b) and (c) because they have inverse slope.
_____________________________________
6)
The equation is in the form: y=mx+b
m = (4-2) / (4-4) = ?
There is no slope but x=4, then the equation is x=4.
_____________________________________
7)
The slope is m=-3
When the line is perpendicular, the new slope is:
m' = -1/m
m' = -1/-3
m' = 1/3

The point (0, 5) belongs to the equation:
y=m'x+b
5=1/3(0)+b
b = 5

The equation is: y=x/3 + 5
_____________________________________
8)
2x-3y = -6
3y = 2x+6
y = (2x+6)/3
f(x) = (2x+6)/3
_____________________________________
9)
There is no slope and no y-intercept.
_____________________________________
10)
m = (1-2) / (15-4)
m = -1/11
=>
y = mx + b
1 = -1/11(15)+b
1 = -15/11+b
11/11 = -15/11+b
b = 11/11+15/11 = 26/11

The equation is y= -x/11+b, with b different from 26/11.

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Answer 8

Looking for easy answers on the Internet won't help you understand the subject. Get yourself a good maths book of which there are thousands out there, and if you still have problem with questions of the sort you are posing, then better say good-bye to maths.

Answer 9

1-2. slope is rise over run.. graphing it may help you
3. solve them and graph
4.to find y-intercept make x=0
5. same as no. 3

good luck with the rest.. a book may help you understand more.

Answer 10

I think you better do your homework to make you understand the topic better.