Question

A line passes through the points (1, 4) and (3,-4). Which is the equation of the line?

O y=-4x+8
O y=-2x + 6
O y=-1/4x+2
O y = 2x + 2

Answer 1

y = -4X + 8

Explanation:

Take each point and substitute for x and y. If (x,y) then 4 = -4(1) + 8 is true and -4 = -4(3) + 8. Both points satisfy the equation therfore the line passes through both points.

Answer 2

y = -4 x + 8

which agrees with the first answer in the list.

Explanation:

We first calculate the slope via the quotient formula:

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

which for our case gives:

Slope = (4 - -4) / (1 - 3) = 8 / (-2) = -4

The we calculate the y intercept by using any one of the given points (for example (1, 4)) in the general formula of a line in slope-intercept form:

y = m x + b

y = -4 x + b

4 = -4 (1) +b

4 = -4 + b

b = 4 + 4

b = 8

Then the final expression for the line becomes:

y = -4 x + 8