Question

graph this line.
$y - 4 = 4(x + 2)$
click to select points on the graph.

Explanation:

Step1: Identify the form of the line equation

The given equation is \( y - 4 = 4(x + 2) \), which is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(- 2,4) \) and the slope \( m = 4 \).

Step2: Find a point on the line

From the point - slope form, we know that when \( x=-2 \), \( y = 4 \). So the point \( (-2,4) \) lies on the line.

Step3: Use the slope to find another point

The slope \( m = 4=\frac{\text{rise}}{\text{run}}=\frac{4}{1} \). Starting from the point \( (-2,4) \), if we move 1 unit to the right (increase \( x \) by 1) and 4 units up (increase \( y \) by 4), we get the point \( (-2 + 1,4+4)=(-1,8) \). If we move 1 unit to the left (decrease \( x \) by 1) and 4 units down (decrease \( y \) by 4), we get the point \( (-2-1,4 - 4)=(-3,0) \).

To graph the line, we can plot the points we found (for example, \( (-2,4) \), \( (-1,8) \), \( (-3,0) \)) and then draw a straight line through them.

Answer:

To graph the line \( y - 4=4(x + 2) \), plot the points (e.g., \( (-2,4) \), \( (-1,8) \), \( (-3,0) \)) and draw a straight line through them. The line has a slope of 4 and passes through the point \( (-2,4) \).