Question

Which equation represents the relationship between x and y shown in the table?

Answer 1

y = 2x - 3

Explanation:

why ? we only need to take the equation and an ordered x,y pair, put the x-value into every place of x in the equation and calculate. if the resulting y-value is the same as the one from the x,y pair for all the given x,y pairs, the the equation is correct.

starting with (2, 1) as x,y pair we can eliminate already the first 3 answer options

1 = ½×2 - 4 = 1 - 4 = -3 wrong

1 = ½×2 + 4 = 1 + 4 = 5 wrong

1 = 2×2 + 1 = 4 + 1 = 5 wrong

1 = 2×2 - 3 = 4 - 3 = 1 correct

so, we don't even need to try the other x,y pairs. it can be only the 4th answer option.

Answer 2

y = 2x - 3

===================

Use the table to find the slope of the line first:

• 
  `m=\cfrac{y_2-y_1}{x_2-x_1}`

For any pair of coordinates we get a result of:

• m = 2

Now we can use point-slope form and one of coordinate pairs to find the line:

• 
  `y-y_1=m(x-x_1)`, where we substitute the coordinates with (2, 1)

• 
  `y-1=2(x - 2)`

Convert the equation into slope-intercept form y = mx + b:

• 
  `y-1=2x-4`

• 
  `y=2x-3`