linear equations?

Question

Please help me....i get my homework through the PC and it never told me how to write linear equations.....and now all of a sudden it wants me to answer these questions:

What is the slope of a line parallel to the line whose equation is y - x = 5?

a)-1
b)1/5
c)1
d)5

What is the equation of a line that passes through points (-1, 2) and (5, 2)?


and i dont understand how to even do those

Answer 1

First, you'll need to know the general equation: y = mx +b, where m is the slope of the line. Now, all you need to do is convert the equation you were given into this format.
y - x = 5
Add x to both sides
y = x + 5
...and you have your equation in the y = mx + b format. Your m is 1.

Answer 2

#1

y - x = 5
y = x + 5
The slope is the coefficient of 'x', in this case '1'.
So any line parallel will have the same slope of '1'.
The figure 'one' is not shown in front of 'x'. When an number is not shown it is understood to be '1'(one).

#2
Any linear eq'n has the form y = mx + c
where 'm' is the gradient and 'c' is the intercept on the y-axis.
To find the gradient:
(2-2)/(5--1) = 0/6 = 0 =>the gradient
y = 0x + c
To find 'c', take any point and substitute into the known eq'n.
2 = 0(5) + c
C = 2 - 0(5)
But anything multiplied by zero is zero so 0(5) =0
C = 2
y = 0(5) + 2
Again 0(5) = 0
So y = 2

It is a straight line horizontal to the 'x' axis intercepting the y - axis at '2'.

Answer 3

The equation for a line is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

With that in mind let's look at question 1:

y - x = 5

Move the x over to get it in the form of our original equation:

y = x + 5

So, the slope (m) is 1.

By the same token, your second question needs to fit the form y = mx + b, but you're going to start with (y - y1) = m(x - x1)

Slope (m) = (y2 - y1) / (x2 - x1)

m = (2 - 2) / (5 - -1) = (2 - 2) / (5 + 1) = 0

So, plug the values into the equation:

y - 2 = 0(x - -1)
y = 2

That's your equation, y = 2.

Answer 4

parallel lines have the same slopes, so y-x = 5 can be written as y = 5 + x, and so slope = 1 (c).

Slope = delta y/delta x = 0/6, so line is y = 2. This is not a good example for you to work with. In general, you would compute the change in y-values, the change in x-values, and take the quotient, which becomes the "m" in a line eq'n --> y = mx + b. Then use either given value (x,y) in your eq'n to calculate the "b" constant.

Answer 5

To find the slope you have to set the equation = to Y so you would have:
y=x+5 (by simply adding x to both sides)
The slope in the number in front of the X - in this case it is only 1.

Answer 6

solve for y
y-x=5
y-x+x=5+x
y=5+x
the slope of the line is the multiple of x when the equation is in terms of y (in other words when it is y alone on one side of the eqaution) in this case it's 1
second one is nearly a trick question, please note that the y values are the same, I'll let you solve it from there