Find the equation of Line A. If two lines are parallel, what must be true of their slopes?)

Question

a. Line A passes through (0, -3) and (5, -1). Find the equation of Line A. b. Line B is parallel to Line A. Find a possible equation for Line B. (Hint: There are many possibilities. If two lines are parallel, what must be true of their slopes?)

Answer 1

The slope of a line is given by the formula

m = (y₂ - y₁) / (x₂ - x₁)

So,

m = (-1 -(-3)) / (5 - 0) = (-1 + 3) / (5) = 2/5

Now, using the slope-intercept form of a linear equation:

y = mx + b

we can substitute either coordinate for x and y respectively and solve for b, because any point on that line must obey that equation.

(0,-3) makes the arithmetic easier:

-3 = (2/5)*(0) + b = 0 + b = b

So, y = (2/5)x -3

To check, we could use the other coordinate:

-1 = (2/5)*(5) -3= 2 -3 = -1

Some other tutor may wish to demonstrate this using the point-slope form of a linear equation, and I welcome this.

Finally, parallel lines have the same slope but different y-intercepts:

y = (2/5)x + 4 is one such paralel line.

If the y-intercept AND the slope are the same, then you can say that the lines are the same or, equivalently, that they are coincident.