Math Problem STRAIGHT LINES - Help :)?

Question

Hi, i've been given this question by my teacher and I just can't get what its asking me. I really need help on the theory side as I want to be able to do it with out getting confused like I am.

The Equations of four straight lines are:

3x - y = 5
y = x + 4
2y = x - 10
y = 3x + 1

i) One or more of the lines go through the point (0,-5). Write down the equation of the line/lines which pass through (0,-5)

ii) Two of the lines are parallel. Write down the equation of these lines.

Thanks! I just have no idea how to tackle it

Answer 1

This is sort of a two part problem. The first step is solving all the equations for y (so they all have the form y= (everything else). Two of them are already in that form, and the rest of the problem will be easier after that.



So you can check your answers you should have the four equations:



y=3x-5

y=x+4

y=.5x-5

y=3x+1



Now you can answer both questions.

The first one is to plug zero into the x and see which one results in a y of -5. This is also called the y intercept of the equations. In the first one, 3*0-5 is -5 so it works, the second 0+4 is 4, the third 0.5*0-5 is -5 (so it works) and in the last 3*0+1 is 1 so it doesn't. The key here is to notice that in that form y=b*x+a when x is zero it doesn't matter what a is, a determines the y intercept.



Then they want to determine which lines are parrallel. To do this you will need to find the slope or graph them. If you want to graph them go ahead. To find the slope, we have y values for all four when x = 0 solved (we did that in part 1) and now we need another value (you can pick anything but if we do x=2 in this case all the numbers will be integers).



So using 2, we get 3*2-5 or 1 or a rise of 6 (1-(-5)) and a run of 2 (2-0)for a slope of 3.

In the second 2+4 is 6. So we have a rise of 2 (6-4) and a run of 2 (2-0).

In the third, x=2 y=0.5*2-5 means y=-4 so our rise is 1 -5-(-4) and our run is 2 so the slope is .5

In the final one x=2 so y=3*2+1 y=7 and our rise is 6 (7-1) and our run is 2. The slope is 3, as it was in the first equation.



Since the first and fourth equations have the same slope (3) they are parallel.



In this part the thing to note is that when the equations are listed y=b*x+a b is the same as the slope. Remembering both means that you don't have to do all the arithmatic.



Looking at them with our short cut:



y=3x-5 slope of 3 y intercept of -5 (it goes through 0,-5)

y=x+4 slope of 1 y intercept of 4 (it goes through 0,4)

y=.5x-5 slope of 0.5 y intercept of -5 (it goes through 0,-5)

y=3x+1 slope of 3 y intercept of 1 (it goes through 0,1)



Good luck with the rest of your problems!

Answer 2

OK...For the first part, substitute x=0 and y=-5 and see which of the equations comes out correct. If you get 3=7, then you know that the line does NOT go through the point (0,-5). You have to get 3=3 or some other true statement.



For the second one, parallel lines have equal slopes. Put each of the four equations into the form y=mx+b. For example, in the first equation, 3x-y = 5 subtract 3x from both sides -y = -3x+5 multiply both sides by -1 so that y=3x-5 and there's your y=mx+b. M is the slope, so the slope of that line is 3. Do that with the other three. Two of the lines will have the same slope and those two are parallel.



If you are still confused, ask your teacher if he can arrange for some tutoring. The more confused you are, the more confused you'll get because math builds on itself. You need to catch up. Good luck.

Answer 3

First put each of these lines in Slope-Intercept Form: y = mx + b where m is the slope and b is the y-intercept..



1. 3x - y = 5 ----> y = 3x - 5

2. y = x + 4

3. 2y = x - 10 -------> y = (1/2)x - 5

4. y = 3x + 1



i) Determine which lines pass through (0,-5). This is really easy now since we put them in Slope Intercept Form b/c all we have to do is look at the y-intercept ('b') in the equation.. In looking at the equations we can easily tell that equation 1 and 3 pass through (0, -5)..



ii) Lines are parallel if they have the same slope. In looking at the equations of the lines, we can easily tell that equations 1 and 4 have similar slopes --- that being 3...

Answer 4

first of all re arrange the euqations into the equation for a line (y=mx + c, where x and y are co-ordinates, m is the gradient of the line and c is the y-intercept). The equations are:

y=3x-5

y=x+4

y=0.5x-5

y=3x+1



i) To solve this, input 0 as x into the equations and find which one produces an answer of -5. (The answer is y=3x-5 and y=0.5x-5)



ii) This is simpler than it looks. The gradient of a curve changes depending on its steepness. Two lines with equal gradient will always be parallel. (The answer is y=3x-5 and y=3x+1)

Answer 5

i) Put (0,-5) and check which one is satisfied (lines1 and 3)



ii) lines 1 and 4 are parallel, they have the same slope. You know abt slopes?

Suppose the equation of a line is like this: a*x+b*y+c = 0. Write it in this form: y = -(a/b)*x-(c/b)

the slope = -(a/b) and the line cuts the y axis at point (0,-(c/b))...

Answer 6

These two go through (0,-5):

3x - y = 5

2y = x - 10



These two are parallel:

y = 3x + 1

3x - y = 5



All you have to do is get y by itself on one side of the equation and then graph them on a basic x,y axis up to 10 and get your answers. It took me 3 minutes.

Answer 7

can u draw the graph? that should make it easier



if not put 'x' in as 0 and see which y comes out as -5 (i can see 2y=x-10 is one answer)



as for the parelell i dunno apart from drawing the graphs...





(ask your teacher) :P