Question

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

Answer 1

Answer:

y = 5

Step-by-step 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