Question

graph this line:
$y + 3 = -\frac{5}{7}(x - 2)$

Explanation:

Step1: Identify the form of the line equation

The given equation is \( y + 3 = -\frac{5}{7}(x - 2) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. Here, \( m =-\frac{5}{7} \) and the point \( (x_1,y_1)=(2,- 3) \).

Step2: Plot the point

First, plot the point \( (2,-3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m =-\frac{5}{7}=\frac{\text{rise}}{\text{run}} \). From the point \( (2,-3) \), move down 5 units (because the rise is - 5, which means a downward movement) and then move to the right 7 units (because the run is 7, a positive run means a movement to the right). This will give us another point on the line. For example, starting from \( (2,-3) \), \( x = 2+7 = 9 \) and \( y=-3 - 5=-8 \), so the point \( (9,-8) \) is also on the line. Alternatively, we can move up 5 units and to the left 7 units. From \( (2,-3) \), \( x = 2-7=-5 \) and \( y=-3 + 5 = 2 \), so the point \( (-5,2) \) is on the line.

Step4: Draw the line

Draw a straight line passing through the two (or more) points that we have found (e.g., \( (2,-3) \) and \( (9,-8) \) or \( (2,-3) \) and \( (-5,2) \)).

Answer:

To graph the line \( y + 3=-\frac{5}{7}(x - 2) \):

1. Plot the point \( (2,-3) \) (from the point - slope form \( y - y_1=m(x - x_1) \) where \( x_1 = 2,y_1=-3 \)).
2. Use the slope \( m =-\frac{5}{7} \): from \( (2,-3) \), move down 5 units and right 7 units to get \( (9,-8) \), or up 5 units and left 7 units to get \( (-5,2) \).
3. Draw a straight line through the plotted points.