Question

The table shows a linear relationship between x and y

x y
-6 -1
0 -3
3 -4
9 -6

Create an equation that describes the relationship shown in the table.

Answer 1

To find the equation of the linear relationship, we need to determine the slope (m) and the y-intercept (b) of the line passing through the points (-6, -1) and (9, -6).

The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)

Using points (-6, -1) and (9, -6):
m = (-6 - (-1)) / (9 - (-6))
m = (-6 + 1) / (9 + 6)
m = -5 / 15
m = -1/3

Now, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)

Using the point (-6, -1) and the slope -1/3:
y - (-1) = -1/3(x - (-6))
y + 1 = -1/3(x + 6)
y + 1 = -1/3x - 2
y = -1/3x - 3

Therefore, the equation that describes the relationship shown in the table is y = -1/3x - 3.