High School Maths Problem?

Question

hello thanks for any help.

im doing revision questions on the topic "the equation of a straight line in the form of 'y - b = m (x - a)' "

one of the questions is;

Find the equation of the straight line which is parallel to y + x = 10 through the origin.

what is the answer and could somebody please explain to me how you came to that answer?

thanks again,much appreciated.

Answer 1

I'm not sure about the form you're using,  I've always used the slope-intercept form:

y = mx + b

Two parallel lines have the same slope.  So finding the slope of the first line will give you the slope of the second line:

y + x = 10

y = -x + 10

The slope is -1

So the slope of the second line is also -1

It goes through the origin, which is point (0, 0) so we have an x, y, and m. Plug in and solve for b:

y = mx + b

0 = (-1)(0) + b

0 = 0 + b

b = 0

So your equation is y = -x

Answer 2

y + x = 10

so

y = -x + 10

The gradient of this line is -1 because that's the coefficient in front of the 'x' term.

The answer is y = -x because when x = 0, y = 0.

Answer 3

In order to find a line that is paralel to other one, this must happen:

m1=m2 This mean, that the slope of the second line is equal to the slope of the first line

If the first line is:

y+x=10 or y=10-x then the slope m1=-1(value next to the x)

So, the second slope will be:

m2=m1

m2=-1

m2=-1

Now, the secon line cross through the origin, in other words through the point (0,0)

Finally to find the second equation, you need to use tyhis formula and replace the point and the slope

y-y1=m(x-x1)

y-0=-1(x-0)

y=-x and this is the answer

i hope this can be useful

David