Line AB contains points (2,1) and (-1,-8). What is the equation of the line parallel to line AB that contains the point (0,2)?

G e n er a l e q u a t i o n f or l in e in s l o p e in t erce pt f or m : y = a x + b T o f in d a an d b s u b s t i t u d e p o in t s ( 2 , 1 ) , ( − 1 , − 8 ) in t o e q u a t i o n { − 8 = − 1 a + b ∣ ∗ − 1 1 = 2 a + b ​ { 8 = 1 a − b 1 = 2 a + b ​ + − − − − A dd i t i o n m e t h o d 9 = 3 a ∣ : 3 a = 3 b = 1 − 2 a = 1 − 6 = − 5 A B : y = 3 x − 5 n e w l in e : y = m x + c i f l in e i s p a r a ll e l m = 3 y = 3 x + c ∣ s u b t i t u t e ( 0 , 2 ) 2 = c A n s w er : y = 3 x + 2

Answered by luana | 2024-06-10

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.

Answered by dulcita2412 | 2024-06-13

The equation of the line parallel to line AB, which passes through the point (0, 2), is y = 3x + 2. This is derived from determining the slope of line AB and using it along with the given point. Since parallel lines share the same slope, we set the slope to 3 and found the y-intercept to be 2.
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Answered by luana | 2024-12-18