Question

graph the equation.
y - 2 = -5(x - 1)
...
use the graphing tool to graph the equation.
(click to enlarge graph)
(graph with x-axis from -12 to 12 and y-axis from -10 to 12, grid lines)

Explanation:

Step1: Identify the form

The equation \( y - 2=-5(x - 1) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(1,2) \) and the slope \( m=- 5 \).

Step2: Plot the point

First, plot the point \( (1,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = - 5=\frac{\text{rise}}{\text{run}}=\frac{-5}{1} \). From the point \( (1,2) \), move down 5 units (because rise is - 5) and then move 1 unit to the right (because run is 1). This gives us the point \( (1 + 1,2-5)=(2,-3) \). We can also move up 5 units and left 1 unit from \( (1,2) \) to get the point \( (1-1,2 + 5)=(0,7) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (1,2) \), \( (2,-3) \), \( (0,7) \)) to graph the equation \( y-2=-5(x - 1) \).

Answer:

To graph \( y - 2=-5(x - 1) \):

1. Identify the point \( (1,2) \) from the point - slope form.
2. Plot \( (1,2) \).
3. Use the slope \( m=-5 \) to find additional points (e.g., \( (2,-3) \) or \( (0,7) \)).
4. Draw a line through these points. The line has a slope of - 5 and passes through \( (1,2) \).