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Chapter 3: Problem 28

For each point-slope equation given, state the slope and a point on the graph. $$ y-4=-\frac{2}{9}(x+5) $$

Short Answer

Expert verified
The slope is \(-\frac{2}{9}\) and a point on the graph is \((-5, 4)\).

Step by step solution

01

Identify the Form

The given equation is in point-slope form: \(y - y_1 = m(x - x_1)\)
02

Extract the Slope (m)

In the equation \(y - 4 = -\frac{2}{9}(x + 5)\), the slope \(m\) is \(-\frac{2}{9}\).
03

Identify the Point (\(x_1, y_1\))

Compare the given equation with the general point-slope form to identify the point. Since \(y_1\) is compared with 4 and \(x_1\) with -5 (note that the equation uses \(x + 5\)). So the point \((x_1, y_1)\) is \((-5, 4)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Slope
In algebra, the slope is a measure of the steepness or incline of a line. It indicates how much the y-coordinate of a point on the line changes for a unit change in the x-coordinate. You can think of the slope as the 'rise over run'. In the equation \(y - 4 = -\frac{2}{9}(x + 5)\), the slope (\

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