Question

Write the standard form of the equation of the line through the pair of points (3,5) and (1,5).

The standard form of the equation of the line passing through the points (3,5) and (1,5) is given by
(Simplify your answer.)

Answer 1

y = 5

Explanation:

The standard form of a linear equation is Ax + By=C

But let's start with the slope-intercept form: y = mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

M, the slope, may be calculated by using the Rise/Run between the two given points: (1,5) and (3,5):

Rise = (5-5) = 0 [Note that the value of y does not change when x = 1 or 3.]

Run is = (3-1)=2

Rise/Run (slope, m) is (0/2) or 0. [y does not change as a function of x. It is a flat, horizontal line]

The equation becomes y = (2/3)x + b

We need to find a value of b, the y-intercept, that forces the line to go through both points. This can be done by entering one of the points into the equation and solving for b:

y = (0)x + b

I'll use (1,5)

5 = (0)*(1) + b

b = 5

The equation becomes y = (0)x + 5 or y = 5

Standard form of the equation is Ax + By = C

A is 0, B is 1 and C is 5

y = 5