Question

The table represents some points on the graph of a linear function. Write a function that represents this relationship.
x= -2, -1, 3, 4, 7 y= -4.5,-7.5, -19.5, -22.5, -31.5

Answer 1

To find the equation of the linear function, we will first calculate the slope using two of the given points:

slope = (change in y) / (change in x) = (-7.5 - (-4.5)) / (-1 - (-2)) = -3 / 1 = -3

Next, we will use the point-slope form of a linear equation to find the equation of the function:

y - y1 = m(x - x1)

Using the point (-2, -4.5):

y - (-4.5) = -3(x - (-2))
y + 4.5 = -3(x + 2)
y + 4.5 = -3x - 6
y = -3x - 10.5

Therefore, the function representing this relationship is:

y = -3x - 10.5