Question

graph the line.
$y - 3 = \frac{4}{3}(x + 1)$

Explanation:

Step1: Identify the form of the equation

The given equation \( y - 3=\frac{4}{3}(x + 1) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(- 1,3) \) and the slope \( m = \frac{4}{3} \).

Step2: Plot the point

First, plot the point \( (-1,3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{3} \) means that for a run of 3 (change in \( x \)) to the right, the rise is 4 (change in \( y \)). Starting from \( (-1,3) \), if we move 3 units to the right ( \( x=-1 + 3=2 \)) and 4 units up ( \( y = 3+4 = 7 \)), we get the point \( (2,7) \). We can also move 3 units to the left ( \( x=-1-3=-4 \)) and 4 units down ( \( y = 3 - 4=-1 \)) to get the point \( (-4,-1) \).

Step4: Draw the line

Draw a straight line passing through the plotted points (e.g., \( (-1,3) \) and \( (2,7) \) or \( (-1,3) \) and \( (-4,-1) \)).

Answer:

To graph the line \( y - 3=\frac{4}{3}(x + 1) \):

1. Plot the point \( (-1,3) \) (from the point - slope form \( y - y_1=m(x - x_1) \) where \( x_1=-1,y_1 = 3 \)).
2. Use the slope \( \frac{4}{3} \): from \( (-1,3) \), move 3 units right and 4 units up to get \( (2,7) \), or 3 units left and 4 units down to get \( (-4,-1) \).
3. Draw a straight line through the plotted points.