Which linear function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)?
f(x) = -2/3x - 11
f(x) = -2/3x - 1
f(x) = -2/3x + 3
f(x) = -2/3x + 13

Solution:

Point slope form is used to represent a straight line using its slope and a point on the line. It means that the equation of a line whose slope is 'm' and which passes through a point (x₁, y₁) is found using the point-slope form.

y - y₁ = m (x - x₁)

where, (x, y) is a random point on the line and m is the slope of the line.

The given point-slope equation is

y + 7 = -2/3(x + 6)

By further calculation

y + 7 = -2/3 x - 4

y = -2/3 x - 4 - 7

y = -2/3 x - 11

This is of the form y = mx +b

Therefore, the linear function which represents the line is y = -2/3 x - 11.