Question

On a coordinate plane, a line goes through (0, negative 1) and (3, 1). A point is at (negative 3, 0).

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

y = Two-thirdsx + 3
y = Two-thirdsx + 2
y = Negative three-halvesx + 3
y = –Three-halvesx + 2

Answer 1

c

Explanation:

Answer 2

Answer: y = (2/3)x + 2

Explanation: We have a line that passes trough the points (0, -1) and (3, 1)

The slope of this line that passes trough the points (x1,y1) and (x2,y2) is:

s = (y2 - y1)/(x2 - x1)

s = ( 1 - (-1))/(3 - 0) = 2/3

So we know that this line has the shape:

Y1(x) = 2/3x + b

where b is the y intercept.

In order to find the value of b, we can do:

Y1(0) = -1 = (2/3)*0 + b = b

so we have that b = -1, and the equation of the line is:

y1(x) = (2/3)*x - 1

Now, we want to find another parallel line that passes through the point (-3,0)

because this new line is parallel to the one we previous had, their slopes must be equal, then the equation of our new line is:

Y2(x)= (2/3)x + c

and we need to find the value of c.

Y2(-3) = 0 = (2/3)*-3 + c = -2 + c = 0

c = 2

then the equation is:

Y2(x) = (2/3)x + 2