Question

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

Answer 1

The linear function that represents the given point-slope equation y + 7 = -(2/3)x + 6 is y = -(2/3)x - 1, which is found by rearranging the equation to the form y = mx + b.

Step-by-step explanation:

The question asks for the linear function that represents the line given by the point-slope equation y + 7 = –(2/3)x + 6. To write this in the standard form of a linear equation, which is y = mx + b (where m stands for the slope and b stands for the y-intercept), we need to isolate y.

Let's rearrange the equation step by step:

1. First, subtract 7 from both sides to get y = –(2/3)x + 6 – 7.
2. Next, combine the constants to simplify the equation: y = –(2/3)x – 1.

This results in the linear function y = –(2/3)x – 1, which is the standard form of the equation given by the point-slope form.

Answer 2

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

First distribute the -1.
y+7= -(2/3)x-6

Then subtract 7 from both sides to isolate y.
y= -(2/3)x-13

Final answer: f(x)= -(2/3)x-13