What is the slope and y-intercept of the equation 3(y - 2) + 6(x + 1) - 2 = 0?

Solution:

We will be using the concept of the slope-intercept form of a line to solve the given question.

Given: 3(y - 2) + 6(x + 1) - 2 = 0

⇒ 3y - 6 + 6x + 6 - 2 = 0

⇒ 3y + 6x - 2 = 0

We need to find the slope of 3y + 6x - 2 = 0 first.

Rewrite the equation in y = mx + c form,

⇒ 3y = -6x + 2

⇒ y = -2x + 2/3

Thus, slope(m) = -2.

To determine the y-intercept we need to substitute x = 0 in the equation: y = -2x + 2/3,

⇒ y = -2(0) + 2/3

⇒ y = 2/3

Thus, the slope and y-intercept of the equation 3(y - 2) + 6(x + 1) - 2 = 0 are -2 and 2/3.

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What is the slope and y-intercept of the equation 3(y - 2) + 6(x + 1) - 2 = 0?

Summary:

The slope and y-intercept of the equation 3(y - 2) + 6(x + 1) - 2 = 0 are -2 and 2/3 respectively.