How do I figure out a linear equation given a table but missing values?

Question

So the table of values is

 

x: 0,   5, 8,   10,     x 

y: x,9.50,x,13.75,25.75

 

In pairs its (0,x) (5,9.50) (8,x) ( 10,13.75) (x, 25.75) 

 

 

 

The question is asking to first write a linear equation between y and x and then fill up the table. 

Answer 1

The fact that it is a linear equation tells us that every point on this table is on the line.  In other words, we need to find the slope between any two complete points.  The complete points that we have are (5, 9.50) and (10, 13.73).  Using the formula for slope to find the slope between these two points.

 

m = (y₂ - y₁) / (x₂ - x₁)

m = (13.73 - 9.50) / (10 - 5)

m = 4.23 / 5

m = 0.846

 

This is the slope.  Now, we can use the point-slope form that applies the slope and any of the points to get the equation of the line.  Use the point (5, 9.50).

 

y - y₁ = m(x - x₁)

 

y - 9.50 = 0.846(x - 5)

 

y = 0.846x - 4.23 + 9.50

 

y = 0.846x + 5.27

 

 

This is the equation of the line.  You can use this equation to find the missing values in the table.

 

For (0, x),    evaluate y when x=0

For (8, x),   evaluate  y when x=8

For (x, 25.75),   evaluate x when y=25.75