Question

graph the line.
$y - 2 = \frac{2}{3}(x - 4)$

Explanation:

Step1: Identify the form

The equation \( y - 2=\frac{2}{3}(x - 4) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(4,2) \) and the slope \( m = \frac{2}{3} \).

Step2: Plot the point

First, plot the point \( (4,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{2}{3} \) means that from the point \( (4,2) \), we can move up 2 units (since the numerator of the slope is 2) and then move to the right 3 units (since the denominator of the slope is 3), or down 2 units and left 3 units. Moving up 2 and right 3 from \( (4,2) \), we get the point \( (4 + 3,2+2)=(7,4) \). Moving down 2 and left 3 from \( (4,2) \), we get the point \( (4-3,2 - 2)=(1,0) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (4,2) \), \( (7,4) \), \( (1,0) \)) to graph the line.

Answer:

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

1. Plot the point \( (4,2) \).
2. Use the slope \( \frac{2}{3} \) to find other points (e.g., \( (7,4) \) by moving up 2, right 3 from \( (4,2) \); \( (1,0) \) by moving down 2, left 3 from \( (4,2) \)).
3. Draw a straight line through these points.