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Question 499756: write an equation that passes through the given point and satisfies the given condition.
(7,1);parallel to y=-x+3
Answer by Flannery(124)   (Show Source):
You can put this solution on YOUR website! Ok, first y=-x+3 is in "point-slope" form.
The format for it is y=bx+c.
The y intercept is the place where y is 3 and x is 0 in this one.
I'll show you.
Find values for x when y = {0,1,2,3,}
0=-x+3
x=3
(3,0) meaning (x value, y value)
The "c" term in "point-slope" tells you the value for x when y=0. In this case 3
now a few more points on the line "y=-x+3"
1=-x+3
x=2
(2,3)
2=-x+3
x=1
(2,1)
3=-x+3
x=0
(3,0)
Plot this on graph paper and its a line passing through the y axis at (0,3) and the x axis at (3,0).
Now to get a parallel.
remember the formula for your equation, y=-x+3
you'll need to "just know" that the "c" term, in this case 3, is always the x value when y=0
you'll need to "just know" that the "b" term, or the coefficient of x is always the slope. In this case the slope is -1.
Slope is rise over run, or the ratio of increase in y over increase in x.
In this case -1 over 1.
So start at (7,1) and start plotting a line with a slope of -1.
The first thing you should come to is the x intercept at (0,8).
Because increase in y is -1 (go down a square) and increase in x is one (go right a square).
Now to plot some more of the second line by useing "point slope".
Negative slopes like this one always slant downward from left to right, and if we keep going down we next hit (9,-1).
What if we backed up? to do so reverse the direction and go up a y value back an x value. we can back up to(6,2),(5,3),(4,4),(3,5),(2,6)(1,7)(0,8) and so on.
If you want to check all this work, there are solvers on the site. My guess is your class already requires you to have a graphing calculator. (I checked this with Microsoft Mathematics, which is a free download).
Anyway this way of getting what you are looking for is the by hand graphing method aka "ol' plug n chug"
Now that we found the y intercept at (0,8) we know enough to write a new equation, y=-x+8
y=-x+8 passes through (7,1) and is paralell to y=-x+3
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