Question

1. $y - 1 = 3(x + 6)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 1 = 3(x + 6) \), which is in point - slope form \( y - y_1=m(x - x_1) \), where \( m = 3 \) (the slope) and the point \( (x_1,y_1)=(- 6,1) \).

Step2: Find two points on the line

• First, use the point from the point - slope form. When \( x=-6 \), \( y = 1 \). So the point \( (-6,1) \) is on the line.
• Second, use the slope to find another point. The slope \( m = 3=\frac{3}{1} \), which means for a change of \( \Delta x = 1 \) (increase \( x \) by 1), \( \Delta y=3 \) (increase \( y \) by 3). Starting from \( (-6,1) \), if \( x=-6 + 1=-5 \), then \( y=1 + 3 = 4 \). So the point \( (-5,4) \) is also on the line.

Step3: Plot the points and draw the line

• Locate the point \( (-6,1) \) on the coordinate grid. Move 6 units to the left of the origin (since \( x=-6 \)) and 1 unit up (since \( y = 1 \)).
• Locate the point \( (-5,4) \) on the coordinate grid. Move 5 units to the left of the origin and 4 units up.
• Then, draw a straight line passing through these two points. The line should have a positive slope (since \( m = 3>0 \)) and will extend in both directions.

Answer:

To graph \( y - 1=3(x + 6) \), plot the point \((-6,1)\) and \((-5,4)\) (or other points found using the slope) and draw a straight line through them. The line has a slope of 3 and passes through \((-6,1)\).