Question About Equations Of Lines?

Question

I have a problem that's written out like this:

x+2y=8

I'm supposed to find the slope, or gradient, and the y intercept. I know how to do it on a formula like y=mx+c but how you would you find it on something like this?

The second part of the question says "find the equation of the line which passes through the points (3,4) and (-2,-11)". Again, I know how to do it with the other type of formula.

If anyone would be so kind to explain it to me? Thanks a lot in advance :)

Answer 1

To find the slope, change the equation to the form in which your more familiar with (y = mx + c)

y = -1/2 x + 4 , m or the slope = -1/2

as for the y-intercept, you can find it just by substituting 0 as the value for x, in this case that will be

y = -1/2 (0) +4
y = 4

For the next question, that'll be in the Two-point form, the formula is

y - y1 = ((y2-y1) / (x2-x1)) * (x-x1)

where: y1 is the y part of the 1st point
x1 is the x part of the 1st point
y2 is the y part of the 2nd point
x2 is the x part of the 2nd point

So that'll be

y - 4 = ((-11-4)/(-2-3)) *(x-3)
y - 4 = ((-15)/(-5)) * (x-3)
y - 4 = (3) * (x - 3)
y - 4 = 3x - 9
y = 3x - 9 + 4
y = 3x -5 , same form as y = mx + c

Answer 2

try this:

x+2y-x=8-x
2y/2=8/2-x/2
y=-x/2+4

The slope is -1/2 and the intercept is 4

second is:

using y=mx+b

4=m3+b
-11=-2m+b

subtract the two equations:
4-(-11)=3m-(-2M)+b-b

15=5m
3=m

solve for b:
4=3(3)+b
4=9+b
b=-5

check:
-11=-2(3)+-5
-11=-6-5=-11 correct

Answer 3

its not really hard... all you got to do is change the problem to look like the formula...

x + 2y = 8
2y = -x +8
y = - 1/2x + 4

now that you got the gradient of -1/2 you can finish the problem...