Question

slope-intercept form of an equation of a line

\\y = -\frac{2}{3}x + 4\\

Explanation:

Identify the slope and y-intercept

The given equation is in slope-intercept form:

$$y = mx + b$$

Comparing \(y = -\frac{2}{3}x + 4\):

$$m = -\frac{2}{3},\quad b = 4$$

Determine key points for graphing

The y-intercept is at:

$$(0, 4)$$

Using the slope \(m = \frac{\text{rise}}{\text{run}} = \frac{-2}{3}\), find a second point by moving \(3\) units right and \(2\) units down:

$$(0 + 3, 4 - 2) = (3, 2)$$

Another point by moving \(3\) units left and \(2\) units up:

$$(0 - 3, 4 + 2) = (-3, 6)$$

Answer:

To graph the equation \(y = -\frac{2}{3}x + 4\):

1. Plot the y-intercept at \((0, 4)\).
2. Use the slope \(-\frac{2}{3}\) (down \(2\) units, right \(3\) units) to plot a second point at \((3, 2)\).
3. Draw a straight line passing through these points.