Slope and Y intercept?

Question

I have a graph with a line with the points .... (0,1) and (1,0) How do I find the slope and y intercept.

Also I have a line that forms a "u" shape with some of the points being.....
(0,0) - (3,-5) - (4,0) How do I find the "vertex point" and any x axis intercepts????

Answer 1

To find the equation of a line, you need 2 things. the slope and a point. we have 2 points and no slope.. so you can put it into the following general equation..

m(x-x1)=y-y1
where x, x1, y, and y1 are x and y values for a coordinate.

m(1-0)=(0-1)
m=-1

now the general equation of a line is.. y=mx+b. we have to find 'b' now.. pick a point, and use the m=1..

1=(-1)(0)+b
b=1

the equation is y = -x+1

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this question already gives you the x intercepts. an x-int is where y=0 and is of the form (x,0) it gives you (0,0) and (4,0).

If we know the roots.. we know that..
x(x-4)=0
-you have to take the reverse steps you normally do when finding the x-intercepts of a parabola with a known-equation..

if you expand it out.. you get..
y= x^2 - 4x

the vertex point is always has an x-value inbetween the two x-ints. so if the two x-values of the x-ints are 0 and 4.. the vertex takes place at x=2.. plug 2 into you equation..
y= (2)^2 - 4(2)
=4-8
=-4

the vertex point is (2,-4)
This question is made a LOT easier with calculus, since the vertex is when the derivative of a function is 0. Given the nature of these problems though, it seems that you're probably not doing these questions in a calculus course. So this is the other way to do it.

Answer 2

Slope is rise/run or change in y over change in x. In this case, change in y is -1 (going from 1 to 0) and change in x is 1 (going from 0 to 1) so you have -1/1 = -1

y-intercept is, by definition, the point where the line crosses the y-axis, or where x = 0. In this case, x = 0 when y = 1, so your y-intercept is 1.

Answer 3

y intercept is when the x value is 0

the vertex point is when the slope equal to 0
the equation for the slope of a function is its first order derivative.
To determine the derivative, you must jump over 10 hoop of fire, 3 snake infested pit and one wide jawed alligator while juggling 3 chainsaw and doing the hula with a hoop around your belly. after doing that, you can find the derivative by the use of a calculus book.
Good luck, not many survive to find the derivative of a function.

Answer 4

Slope = difference in y over difference in x
In other words: y2 - y1/x2 - x1
0-1/1-0 = -1/1 = -1

The slope is -1

Answer 5

x1 = x in first coordinate, etc.
slope = (x1 - x2) / (y1 - y2)
(you can use any two points in any order)
Y intercept is where line crosses y-axis (x = 0).
X intercept is where line crosses x-axis (y = 0).