i need some help on some questions can you help
Hi Kayla;
Linear equations are typically represented in slope-intercept format of...
y=mx+b
m is the slope, the change-of-y divided by the change-of-x.
b is the y-intercept, the value of y when x=0.
For example, if we are provided two points of a line...
(0,5)(5,15)
Our first priority is to establish slope...
(y-y_{1})/(x-x_{1})
(5-15)/(0-5)=-10/-5=2
slope is 2...
y=2x+b
The y-intercept, b, is provided as (0,5)...
y=2x+5
Another format is standard...
Ax+By=C, neither A nor B equal zero and A is greater than zero.
The slope is -A/B. The slope of 2 would be-(2/1) or (2/-1). The negative one is in the denominator because A must be greater than zero...
2x-1y=C
2x-y=C
To calculate C, we would enter either coordinate. I randomly select the second of (5,15)...
[(2)(5)]-15=C
10-15=C
-5=C
2x-y=-5
The the other point is the y-intercept of (0,5). We can use this to verify. Such verification can be performed whether or not it is the y-intercept.
[(2)(0)]-5=-5
-5=-5
The other formula is point-slope...
y-y_{1}=m(x-x_{1})
We will use either point and this will expand into slope-intercept formula. I randomly select the point of (0,5)...
y-5=2(x-0)
y-5=2x
Let's add 5 to both sides...
5+y-5=2x+5
y=2x+5
Let's use the other point, (5,15) to verify results...
15=[(2)(5)]+5
15=10+5
15=15
I HOPE THIS HELPS!
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