I need help with these equations thingy lol?

Question

find an equation of a line that contains (3,-4) and (2,5)

a) y= -9x + 17

b) y = 2x + 1

c) y= -9x +23

d) y= -3x - 5

given the line 3x - 2y = 9, which of the following lines is parallel to it?

a) 2y - 3x = 2

b) 3x+ 2y = 5

c) 3y - 2x = 5

d) 2y + 3x = 9

given the line 3x - 2y = 9, which of the follwing lines is perpendicular to it?

a) 2y - 3x = 2

b) 3y = 12 - 2x

c) 3y - 2x = 5

d) 2y + 3x = 9

if you're not too lazy, do you guys think you can explain it? but you don't have to

Answer 1

you want us to answer 3 of your homework questions and you're implying that WE are lazy ??

Answer 2

find an equation of a line that contains (3,-4) and (2,5)

a) y= -9x + 17

b) y = 2x + 1

c) y= -9x +23

d) y= -3x - 5

narrow it to a or c, since when x goes down 1, y goes up 9, so slope is -9

now just plug in one of the points, if it doesnt work in the one, it's the other:

for a, and the first point: -4 does not equal -27 + 17

for c (just to double check) -4 DOES equal -27 + 23

so C is correct, and I leave it to you to check the correct answer against the second point (2,5) if you want to.

given the line 3x - 2y = 9, which of the following lines is parallel to it?

a) 2y - 3x = 2

b) 3x+ 2y = 5

c) 3y - 2x = 5

d) 2y + 3x = 9

the slopes of parallel lines are equal, so A is correct, for each of them, slope is 3/2 (y = 3/2 x plus something). That means the slope of the lines is the same, but they each start at a different point. You can understand this by using some graph paper and plotting points of each of the two lines.

The way to easily see this is that the 3 is the multiplier of the x, the 2 is the multiplier of the y, they are of opposite signs on the same side of the equation, so with rearrangement, the equation becomes y =  3/2 x plus something (or minus something would also work).

given the line 3x - 2y = 9, which of the follwing lines is perpendicular to it?

a) 2y - 3x = 2

b) 3y = 12 - 2x

c) 3y - 2x = 5

d) 2y + 3x = 9

Parallel lines have the same slope, while perpendicular lines have slopes that, when multiplied together, equal  -1

so the slope of perpendicular lines are negative reciprocals of each other:

the first equation has slope of 3/2, so the perpendicular line has slope

-2/3, which is B (rearrange B to y = 4 - 2/3 x)

Answer 3

Use (3,-4) and (2,5) to get the slope of the line:

m = (5--4)/(2-3)

= -9

Use slope and one of the points to determine y-intercept.

b = y-mx

= -4-(-9)(3)

= 23

Equation of line:

y = -9x + 23

Answer 4

1. C (I just plugged them in)

2. Whatever has the same slope (y=mx+b). The slope of the original equation is  3/2x + -9/2 = y   So the slope is 3/2, which is also the slope of A.

Check: 2y - 3x = 2

2y = 2 + 3x

y = 1 + 3/2x

3. Since you know the slope is 3/2, a line perpendicular would have the slope -3/2, which is answer D

Check: 2y + 3x = 9

2y = 9 - 3x

y = 9/2 - 3/2x)

  

Answer 5

1) see if both coordinates fit into the equation

the answer is c because both coordinates make the answer true

y=-9x+23

-4=-9(3)+23

-4=-4

y=-9x+23

5=-9(2)+23

5=5

2)A parallel line would have the same slope as the original equation.

It may be easier once you change the equations to slope intercept form: y=mx+b (m=slope, b=y-intercept)

-2y=-3x+9

y=3/2x-9/2

a)2y=3x+2

y=3/2x+2

b)3x+ 2y = 5

y=-3/2x+5/2

c) 3y - 2x = 5

y=2/3x+5/3

d) 2y + 3x = 9

y=-3/2+9/2

A) is the answer because it has a slope of 3/2 like the original problem.

3)A perpendicular line is the opposite reciprocal.

Again, change to slope intercept form.

3x-2y=9

y=3/2-9/2

you want to find a slope that is -2/3 because it is the opposite reciprocal (flip the 2 numbers around)

a) 2y - 3x = 2

y=3/2x+2

b) 3y = 12 - 2x

y=-2/3x+4

c) 3y - 2x = 5

y=2/3x+5/3

d) 2y + 3x = 9

y=-3/2x=9/2

B) is the answer because it has a slope of -2/3

Answer 6

its just slope

c

b

b

the secant and third are easy in the secant you need to find the one parallel so the 2 with the same slope so if the numbers are the same there parallel. the third one is the same except  3/2 is perpendicular to -2/3.

btw its not cheating you found a different resource to draw from but don't make a habit of it.