Respuesta :
Answer:
y=-2x+20 or y-4=-2(x-8)
Step-by-step explanation:
first we need to calculate the slope
y2-y1/x2-x1
-6+4/7-8
-2/1
The slope is -2
Nows lets find the y intercept using
y-y1=m(x-x1)
y-4=-2(x-8)
y-4=-2x+16
+4 +4
y=-2x+20
Y intercept is 20
Answer:
I didn't know what form you wanted the line in.
Slope-intercept form: y=2x-20
Standard form: 2x-y=20
Point-slope form: y+4=2(x-8) or y+6=2(x-7)
You gave the points (8,-4) and (7,-6).
That last point was (7,-6) right? I seen (7-6) and just thought you probably meant (7,-6.
Step-by-step explanation:
Equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
To find the slope: I'm going to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference.
I feel like some people like this more than the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]. It is the same thing just a different way to organize things.
So let's do the finding of the slope:
( 8 , -4)
-( 7 , -6)
-------------
1 2
So the slope is 2/1=2.
So we have m=2.
Let's input into our equation y=2x+b.
We need to find the y-intercept. We could do that by using a point on the line. We get to choose between (8,-4) or (7,-6). It does not matter.
y=2x+b with (8,-4)
-4=2(8)+b
-4=16+b
Subtract 16 on both sides:
-4-16=b
-20=b
So the y-intercept is -20.
The equation is y=2x+-20 or y=2x-20 (your pick-same thing).
Now let's also put it in standard form which is ax+by=c where it is preferable to have a,b, and c as integers. (Integers are {...,-3,-2,-1,0,1,2,3,...}.)
y=2x-20
Subtract 2x on both sides:
-2x+y=-20
This is in ax+by=c form.
You could multiply both sides by -1:
2x-y=20.
This is still in standard form.
Let's also go for point-slope form which is y-y1=m(x-x1) where (x1,y1) is a given point on the line and m is the slope.
We already have the slope is 2.
We have two points to choose from. Choose one and go with it. Let's choose (x1,y1)=(8,-4).
y-(-4)=2(x-8)
or
y+4=2(x-8)
Now if you did go with the other point (x1,y1)=(7,-6) it would be:
y-(-6)=2(x-7)
y+6=2(x-7)
You are probably wondering how those are the same lines. Let's confirm. Solve both of them for y.
y+4=2(x-8)
Distribute 2:
y+4=2x-16
Subtract 4 on both sides:
y=2x-16-4
Simplify:
y=2x-20
Now the other line:
y+6=2(x-7)
Distribute 2:
y+6=2x-14
Subtract 6 on both sides:
y=2x-14-6
y=2x-20
