Question

graph the line.
$y + 1 = 5(x - 4)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 1 = 5(x - 4) \), which is in 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, \( m = 5 \) and the point \( (x_1,y_1)=(4,- 1) \).

Step2: Plot the point

First, we plot the point \( (4,-1) \) on the coordinate plane. To find another point, we can use the slope. The slope \( m = 5=\frac{5}{1} \), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), the rise is \( 5 \) (increase in \( y \) by \( 5 \)).

Starting from the point \( (4,-1) \), if we move \( 1 \) unit to the right (increase \( x \) by \( 1 \) to \( x = 4+1 = 5 \)) and \( 5 \) units up (increase \( y \) by \( 5 \) to \( y=-1 + 5=4 \)), we get the point \( (5,4) \).

We can also move in the opposite direction. If we move \( 1 \) unit to the left (decrease \( x \) by \( 1 \) to \( x = 4-1 = 3 \)) and \( 5 \) units down (decrease \( y \) by \( 5 \) to \( y=-1-5=-6 \)), we get the point \( (3,-6) \).

Step3: Draw the line

After plotting at least two points (e.g., \( (4,-1) \) and \( (5,4) \) or \( (4,-1) \) and \( (3,-6) \)), we draw a straight line passing through these points.

Answer:

To graph the line \( y + 1 = 5(x - 4) \):

1. Plot the point \( (4,-1) \) (from the point - slope form).
2. Use the slope \( m = 5 \) to find another point. For example, from \( (4,-1) \), move 1 unit right and 5 units up to get \( (5,4) \), or 1 unit left and 5 units down to get \( (3,-6) \).
3. Draw a straight line through the plotted points.