Answer :
[tex]General\ equation\ for\ line\ in\ slope\ intercept\ form:\\\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (2,1),\ (-1,-8)\ into\ equation\\\\
\left \{ {{1=2a+b}\ \ \ \ \atop {-8=-1a+b\ |*-1}} \right.\\\\ \left \{ {{1=2a+b}\ \ \ \ \atop {8=1a-b}} \right.\\\\
+----\\\\Addition\ method\\\\
9=3a\ \ |:3\\\\
a=3\\\\
b=1-2a=1-6=-5\\\\
AB:\ y=3x-5\\\\
new\ line: \ y=mx+c\\ if\ line\ is\ parallel\ m=3\\\\
y=3x+c\ \ \ | subtitute\ (0,2)\\\\
2=c\\\\
Answer: y=3x+2[/tex]
Answer:
Step-by-step explanation:
(2, 1 ) and (-1, -8) are on the line AB
Find the slope of the line by substituting the given values in the slope formula:
m= (y2 - y1)/(x2 - x1)
m= (-8 - 1 )/(-1 - 2)
m= 3
By Point slope form:
y - y1 = m ( x - x1)
y - 1 = 3 ( x - 2)
y = 3x - 5 This is the equation of the line AB.
The line parallel to y= 3x - 5 that pases through ( 0, 2 ).
Parallel lines have equal slope, so the slope for both lines is 3.
Now, we have:
Using point slope form ( 0, 2 )
y - 2 = 3 (x - 0)
y= 3x + 2
The equation of the line that is parallel to line AB is : y = 3x + 2.
