Question

Examine the graph at right.

a) Find the equation of the line.
b) Is the line y = 3x+1 parallel to this line? How do you know?
c) Find the equation of the line passing through the points
(4,3) and (-1,1).

Answer 1

a) y= -3x+2

b) no. the two lines don't have the same slope.

c) 5y-2x-7=0

Explanation:

a) We have two points (0,2) and (1,-1).

find the slope of the line: (-1-2)/(1-0)=-3

we already have the y-intercept as 2, so we have the line ready:

y=-3x+2

b) parallel lines have equal slope. here this line has a slope of -3 and the other given line has slope 3. thus, they cannot be parallel. a simpler way of seeing this is the fact that the given line is sloping downwards and thus has a negative slope, and so it can't have a slope of 3.

c) we are given (4,3), (-1,1)

find the slope: (1-3)/(-1-4)=2/5

to find y-intercept, we can use this equation:

1=-1(2/5)+C

C=1+2/5=7/5

so y=2x/5+7/5 or 5y-2x-7=0