Question

graph this line:
y - 7 = -4(x - 1)
click to select points on the grap

Explanation:

Step1: Identify the form of the equation

The given equation \( y - 7=-4(x - 1) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(1,7) \) and the slope \( m=-4 \).

Step2: Find a point on the line

From the point - slope form, we know that the point \( (1,7) \) lies on the line.

Step3: Use the slope to find another point

The slope \( m = \frac{\text{rise}}{\text{run}}=-4=\frac{- 4}{1} \). Starting from the point \( (1,7) \), we move down 4 units (because the rise is - 4) and 1 unit to the right (because the run is 1). So the new point is \( (1 + 1,7-4)=(2,3) \). We can also move up 4 units and 1 unit to the left: \( (1-1,7 + 4)=(0,11) \).

Step4: Graph the line

Plot the points \( (1,7) \), \( (2,3) \), and \( (0,11) \) (or any two of these points) and draw a straight line through them.

Answer:

To graph the line \( y - 7=-4(x - 1) \):

1. Identify the point \( (1,7) \) from the point - slope form.
2. Use the slope \( m=-4 \) to find additional points (e.g., \( (2,3) \) or \( (0,11) \)).
3. Plot the points and draw a straight line through them.